If you are just transferring points from Amex and then redeeming for a mileage award you are definitely not “building up an account” with that airline. This will be purely a transaction, not a relationship. Kind of like a “one-flight stand.”

There are many options here. The first order is finding an airline that offers award availability that works for you and then next is figuring out if/how to transfer Amex to a partner that will let you book. Frankly I think Star Alliance is better for maximum global coverage (but with LatAm weakness IIRC), and Aeroplan is a good Amex partner to use, but you could also use Singapore and probably others. But redemption levels, transfer rates, and fees will vary between programs. Also you need to consider whether the FFP is an “instant transfer” partner of Amex and what the award booking process is (ie, can you put an award on hold while you transfer the points).
It can be a fair amount of work, and the reco to use a service to help you is not a bad one.

Also, this probably belongs in the Amex forum, i’ll alert a mod.