A word to describe an excessively formal process or procedure

Onerous is defined by Oxford Dictionaries as:

(of a task or responsibility) involving a great deal of effort, trouble, or difficulty. ‘he found his duties increasingly onerous’

And by Google as:

(of a task, duty, or responsibility) involving an amount of effort and difficulty that is oppressively burdensome.

labyrinthine

Oxford Living Dictionaries gives the following definition:

1 (of a network) like a labyrinth; irregular and twisting.

‘labyrinthine streets and alleys’

1.1 (of a system) intricate and confusing.

‘labyrinthine plots and counterplots’

‘In the process, he unravelled the labyrinthine means by which a painting bought by war profiteers and sold to German army looters found its way into the cultural heart of Britain.’

‘For a show that has the labyrinthine, seemingly nonsensical plots of a soap opera, that's a real accomplishment.’

‘The country's legendary bureaucracy is as labyrinthine as ever, and its legal system opaque, with separate laws for foreign and domestic investors.’

‘The labyrinthine diplomacy and politics of the Italian wars are the real subject of this painstaking book about what Jem meant to others.’

...

Labyrinthine, through its maze analogy, suggests unnecessary complexity and a process that could be made much more simple.

In almost all cultures and countries on this planet, what you're describing would simply be called bureaucracy and a process that involves a lot of bureaucracy would be referred to as a bureaucratic process. Here's one of the several definitions of this term from the Cambridge Dictionary:

complicated rules, processes, and written work that make it hard to get something done

Example sentence (taken from the English Oxford Living Dictionaries):

More than 3,600 staff will be given the chance to influence the way the trust is run by pointing out the unnecessary rules, paperwork and bureaucracy which slow them down.

By the way, the corresponding idiomatic term for bureaucracy would be red tape. And believe it or not, it can be a single word if you properly hyphenate it and use it as an adjective: red-tape procedures. Here's what they say about this expression on Wikipedia:

Red tape is an idiom that refers to excessive regulation or rigid conformity to formal rules that is considered redundant or bureaucratic and hinders or prevents action or decision-making. It is usually applied to governments, corporations, and other large organizations.

Cumbersome would be a simple word to use here. In your context, cumbersome would mean something that is slow or complicated, and therefore inefficient.

Usage example - 'Most of the employees were vexed with their company's cumbersome procedures'

red tape is defined by Merriam-Webster as:

Official routine or procedure marked by excessive complexity which results in delay or inaction.

Merriam-Webster example of red tape in a sentence:

You would not believe the red tape involved in getting the required permits.

'Convoluted' might be the word you're looking for. Described by Google as:

(especially of an argument, story, or sentence) extremely complex and difficult to follow.

An example of usage:

"the film is let down by a convoluted plot in which nothing really happens"

Employees complain that this methodology is ??? and therefore it would be tiresome to follow it due to the fact it has many phases.

Rigorous - adjective - from the the Cambridge Business English Dictionary:

• detailed and careful:

  1. I want rigorous financial analysis of the options.
  2. The selection process is extremely rigorous.

• strict or severe:

  1. A rigorous monetary and fiscal policy should encourage efficiency.
  2. Refrigeration of food, improved hygiene and rigorous standards in the food industry prevent gastro-intestinal infections.

Meticulous may be ideal here. It is defined as "taking or showing extreme care about minute details; precise; thorough" (dictionary.com).

Or, perhaps Superfluous would be an appropriate word, meaning "being more than is sufficient or required; excessive" or "unnecessary or needless" (dictionary.com). However, this word would be more effective if describing unnecessary procedures, rather than necessary albeit annoying procedures.

Merriam–Webster gives the second, and more distinctive, meaning of rigmarole as "a complex and ritualistic procedure that is characterized more by form than genuine meaning". It often applies to official procedures that, over a long period of time, have adapted to changing circumstances by accumulation, because no-one has had the authority to adapt them by radical simplification.

One might describe such a procedure as anfractuous:-

characterized by twists and turns; convoluted [Collins English Dictionary via the Free Dictionary]

I believe the American taxation system was once so described by a famous politician as an anfractuousity but sadly can't run down the quote; it must be quite old though as words like that don't fit well in a sound bite. Even the spell-checker here doesn't like it.

tedious: takes a lot of time, requires doing a lot of steps that individually aren't too bad, but the sheer number of them is very unpleasant

boring and tiring, esp. because long or often repeated:

https://dictionary.cambridge.org/us/dictionary/english/tedious

And a summary of the other answers:

byzantine: the rules are obscure and/or difficult to understand.

bureaucratic/red tape: it involves getting approval from a lot of other people

convoluted: the process is complicated

labyrinthine: a stronger form of "convoluted"

onerous: requires a lot of effort

cumbersome: inconvenient; have to put a lot of effort into making it work

Possibly 'tortuous', meaning that it has very non-straightforward path, though it doesn't imply anything about subprocesses. Also as a bonus (?) it reads similarly to 'torturous' which (metaphorically) might also describe such a process.

Many of the other answers are unusual words to find in a business setting -- a bit poetic.

I'd suggest involved -- which is defined as "difficult to understand; complicated" -- but which I interpret as "I understand it but it's long and not worth going into, not worth explaining here."

So, "employees complain that this methodology is too involved".

Another synonym is "time-consuming".

A word borrowed from the arts could be used figuratively.

Baroque:

In the decorative arts there is an excess of ornamentation. The departure from Renaissance classicism has its own ways in each country. But a general feature is that everywhere the starting point is the ornamental elements introduced by the Renaissance. (Wikipedia, emphasis added)

Baroque is used often to describe things of any sort that have become too complex (cut-off criteria left as exercise to the reader):

Baldwin’s fastidious thought process and his baroque sentences suddenly seemed hopelessly outdated, at once self-aggrandizing and ingratiating. (New Yorker)

This adjective is specifically applicable to artwork, as at this question: Word for “decorated too much”, but can be extended to describe other nouns. A person can be said to be "baroque", for example:

...it is unclear exactly where the truth lies in the different accounts of the final meeting between Mr. Bo and Mr. Wang, the police chief. Mr. Bo is known to be both baroque and shrewd, and he could have reacted in any number of ways in the meeting, people familiar with the two men say. (NYT)

Answering you question directly, a process such as maneuvering can be "baroque"; here is an example of this use:

The impeachment process, which stretched out over several years, involved some baroque political maneuvering, and ended with Hastings’s acquittal. (New Yorker)

You could consider using Rococo figuratively, but it's descriptive power seems to be much more limited than baroque, at least in common use:

Rococo (/rəˈkoʊkoʊ/, also US: /ˌroʊkəˈkoʊ/), less commonly Roccoco or Late Baroque, is an exceptionally ornamental and theatrical style of architecture, art and decoration which combines asymmetry, scrolling curves, gilding, white and pastel colors, sculpted molding, and trompe l'oeil frescoes to create surprise and the illusion of motion and drama. It is often described as the final expression of the Baroque movement. (Wikipedia, emphasis added)