On verb/subject agreement in an inverted sentence

The resolution is that the subject is singular. But the plural agreement is acceptable too, in this case.

Similar examples with the verb in the singular

At stake is more than just boundaries or GNP.
^{From the Corpus of Contemporary American English (COCA)}

At stake is more than the careers of the two men concerned.
^{From Canada's House of Commons debates}

Similar examples with the verb in the plural

At stake are more than half the delegates needed to win the Democratic nomination.
^{From the Corpus of Contemporary American English (COCA)}

At stake are more than just economies.
^{From U.S. Congressional Record}

Let's shorten your sentence first a bit, while retaining all the main properties. So, let's consider

[1] At stake is much more than jobs.

Let's put this sentence in the canonical, subject-first form:

[2] Much more than jobs is at stake.

To my ear, at least, changing the verb to plural produces a sentence which is not acceptable English:

[3] ^*Much more than jobs are at stake.

I would be curious to know if others disagree with this. There is reason to think some might, for I found these examples:

Yet much more than words are needed.
^{From 'Hearings Before the Committee on Foreign Relations, United States Senate', 1965 (source)}

So much more than words are lost in the translation.
^{From Sierra Club Bulletin, Volume 62, 1977 (source)}

At any rate, it seems that when the subject is postposed, the plural verb becomes acceptable:

[4] At stake are much more than jobs.

Discussion

There are various circumstances in English where the assignment of singular or plural is in some way non-standard; we refer to these as overrides. These are sometimes optional and sometimes obligatory.

Obligatory overrides happen for example with number-transparent non-count quantificational nouns. A typical example is illustrated in

[5]  i  [A lot of work] was done.
      ii  [A lot of errors] were made.

In [5], the number agreement is determined by the oblique, the noun phrase (NP) that is the complement of of. Here are some other nouns that can function similarly to lot in this respect: plenty, lots, bags, heaps, loads, oodles, stacks, remainder, rest, number, and couple (CGEL, pp. 349-350).

Here is another example with an obligatory singular override, this time with a formally plural measure phrase :

Twenty dollars seems/^*seem a ridiculous amount to pay to go to the movies.

But the override is optional in

That ten days we spent in Florida was/were fantastic.

Another example of an optional singular override is

[6] [One in a hundred students] takes/take drugs.

Here the head of the subject is the plural noun students, and simple agreement would dictate a plural verb. But [6] happens to be synonymous with either of

[7]  i  [One student in a hundred ] takes/^*take drugs.
       ii  In a hundred students, [ only one] takes/^*take drugs.

in which, by simple agreement, the verb must be singular. This, plus the presence of one, is presumably why the singular override is possible in [6] (CGEL, p. 504).

And here is an example of an optional plural override:

[8] The committee has/have not yet come to a decision.

The noun committee is singular, and so simple number agreement would dictate a singular verb. CGEL explains it as follows (p. 502):

The optionality of the override with collectives reflects the fact that there is potentially a difference of meaning between the versions with singular and plural verbs. From one perspective a committee is a single entity, but since a committee (normally) consists of a plurality of members it can be conceptualised as denoting this plural set. The construction with a plural verb focuses on the members of the committee rather than on the committee as a unit. The plural override is therefore not permitted with predicates that are applicable to the whole but not to the individual members; it is, moreover, of questionable acceptability if the collective has one (or a/another) as determiner:

[10]  i  The committee consists/^*consist of two academic staff and three students.
         ii  This committee, at least, is/^*are not chaired by one of the premier's cronies.
        iii  One committee, appointed last year, has/^?have not yet met.

Note that these doesn't exhaust the list of constructions that feature overrides; see CGEL for more (pp. 501-507). Having said that, interestingly, neither CGEL nor ComGEL record the optional override with more than constructions like in your question.