The cap for how much a single player can be offered definitely needs a bit of a bump. When a team can sign multiple players in FA to the highest possible offer and STILL have practically half their cap space completely empty, the ceiling needs to be raised. I would set it to at least 15% of total cap space, if not 20%. The starting salaries in the league creation drafts also need to be upped to strengthen the initial market. I'm resigning 100 rated players for pennies in young leagues, and so there's really no way for the market to ever begin to set itself since the only way good players hit the market is via inactive or careless owners.

It's hard for other teams to come in and compete when the top teams in the league all have $50M+ in free cap space for the rare moments when there are FAs worth fighting for.

I agree there's an issue there, however I think the problem is more about players resigning for so cheap:

Free Agent Signing:
http://cust10.myfootballnow.com/player/2711 - RB 84/94 $82M over 6 years Max Contract

Extended Contract:
http://cust10.myfootballnow.com/player/1027 - RB 86/88 $13M over 6 years

The only time a half decent player becomes a free agent is when the owner is inactive. I think that shows a bit of an imbalance. (edit - or when they're getting old).

Every season I sign my vets for less and less...like real life???

It was my understanding that player's resigning requests are based off of the market value for their highest rated position (which I do think is a cool idea), hence my suggestion to increase the potential value of players on the market as well as their initial contracts with the understanding that this would eventually trickle down to all the ones NOT hitting FA.

This is true, they base their requests by the relative salaries of players in their position and similar skills. I think the solution might be to raise the maximum offer, and possibly have them request a bit higher than the algorithm is currently giving them.