I think it would be neat to have FA's motivations not be solely about the dollars. As it stands, other factors kick in only in the event of a tie (which 99.9% only happens with max contracts). I propose that other factors kick in always as an arbitrary dollar amount (but behind the scenes, with exact amounts undisclosed to us owners).
Examples (and I believe that most of these are already programmed as tie-breakers)
Ballparks -- perhaps depending on the particular player, a pitcher might be willing to sacrifice $5-10M off the total contract to pitch in Burlington over Colorado. This doesn't really give anyone an advantage as hitters parks would have the same positive effect on position players, whereas neutral parks would be more of a balance.
Pitching/Hitting Coach -- same concept. Puts a little more weight on getting good ones, especially if you're a vet team who doesn't really have anyone on the ML roster under 27 and doesn't much care otherwise.
Record in previous season -- I know this reeks of making the strong stronger, so perhaps this could have less impact in most cases, though I like the idea of 34yo+ vets taking less to chase the ring; especially if they've never won one. Double the effect if this kind of player passes the first set of cycles without a single offer that meets his initial demands.
No trade clause -- (maybe this already works this way, but I'm pretty sure it does not) being as how it can be quite a nuisance IMHO, it should have a dollar value. Trick here would be not making it worth so much that every FA ends up with one otherwise trading vets would become a nightmare.
Player options -- should be worth a good deal. I've never ever had a reason to offer one other than to a max player. Unless I'm missing something, there is absolutely no good reason to right now. Side note: mutual option seems pretty broken to me in that it is treated exactly the same as a guaranteed year when it's really only 25% guaranteed.