If you offer them the ST invite?

Bueller?

I don't think ST Invite will help you but that's only a guess. 

ive never seen it help you sign anyone for less

I want to say either 5% or 10% GT.  Try 10%, if that doesn't work, bump up your offer a bit until they accept.  I'm not sure the ST invite matters much.  All of that assumes they will sign for "slot".  If a guy is undecided I don't think they'll sign for anything less than their initial demands.  Can't remember about the guys who "want to be drafted in the 1st 5 rounds" they may sign for less than slot, provided that you drafted them in the first 5 rounds.

Most will sign for 85% of asking price, some very slightly lower.  I always offer the STI but not sure it helps.

I NEVER pay full asking price on a guy who says he will sign.

Also, you don't have to up your offer if he refuses initially.  Just offer him the same over and over until he accepts (assuming it's 85% or so + of asking price)