What does "Way beyond seeking" mean?

The phrase is deliberately ambivalent, for the effect of a word play. The word "way" can mean path, direction, system, or process, or it can mean excessively. It is an especially witty title because it illustrates a Tao virtue of economy of expression.

Rephrasing both meanings, we have to use more words:

Taoism is a path for you to overcome your spiritual seeking.

Taoism is so much more than seeking spiritual meaning.

The title of the work suggests that, by reading it, one can go beyond merely seeking enlightenment, and implies that through Taoism one can actually find enlightenment.

Ambiguity is often an important element in spiritual matters, but in this instance it seems merely to be an attempt (perhaps not entirely effective) to imply that through Taoism the seeker can actually attain the enlightenment which the Taoist philosophy claims to offer.

It certainly does show an economy of expression: but perhaps it is not attempting to be witty, in doing so, but may in fact be attempting to suggest that attainment is possible without falling into the trap of actually saying so (as that might possibly entitle a dissatisfied reader to ask for his money back!)

The Dao is written in what looks like paradoxes and requires reflection to understand the inner meaning of the verses.

The first line of the Dao is:

The Dao that can be walked is not the true Dao.

To walk here can mean seek. Hence we have:

The Dao that can be sought is not the true Dao.

Since one of the meanings of Dao is 'Way', this is:

The Way that can be sought is not the true Way.

So the Way is beyond seeking. The author is compressing this into:

The Way beyond Seeking.

It's simply the first line of the Dao.