Is "best gear this project to you" a proper saying?

Solution 1:

So that I can best gear this project to your expertise, can you tell me how much experience you have with list of technical skills?

The problem is that "best gear" looks either like a noun or a compound verb.

John wore his best gear to the match. (his best clothes - BrE)

John best-geared his new car. (??? he replaced his gearbox with the best on the market???)

You are using "gear" to mean "suit" or "tailor". In other words you are using it as a verb. Because this usage is not common, especially with this word-order, it is easy to misunderstand.

Summary

What you intend

So that I can gear this project best to your expertise ...

What people may read

So that I can "best-gear" this project to your expertise ...

For someone fluent in English, they will soon realise what you mean. However I must admit, when I first saw the title of your question, I was puzzled by it. Someone who is not so fluent will soon be on this website asking what on Earth you meant!

Solution 2:

I don't have a problem with "gear X to Y" where Y is something like "your expertise" (rather than "you").

It appears OED doesn't, either:

4. a. To put (machinery) into gear (see gear n. 7); to connect by gearing. Also figurative, to adjust, correct or co-ordinate; spec. to adjust or adapt (something) to a particular system, situation, etc.; to bring into dependence, conformity or harmony; frequently in passive.

You're using it in this sense: adapting the project to suit the skills your correspondent has. OED's earliest citation for that usage is from 1945, so it's not very old, but hardly novel.