Legally Moses can't have anything to do with the TPA and no TPA can legally be aligned with a contract. If TPA and contracts are linked the clubs are in breach of the salary cap rules.
I am not stupid enough to think that it doesn't go on behind closed doors; however, you would be a bit stupid to rely on TPAs gettign a contract over the line when it is your livelihood.
Most of the "bonuses" that come with selecting one club over another in present times are related to other intangibles; like financial advice, investment opportunities, etc.
TPAs are contracts directly between players and the sponsors - check out the Deep Dive on TPAs for the detail.