Yeah, a couple of thoughts on this notion, as I've a history of starting leagues with a clean slate, i.e. no histories, no service times, no anything. You do generally end up with a league full of financial rookies, funneling into quite a year of arbitrations down the road, but the free agency market is always a bit surprising; great if you sim, and quite the wait if you don't.
What wellsoliver may be interested in trying- I haven't, so don't know if it'd work -is to go ahead with your inaugural in whatever fashion you'd like, advance a day or two, then clear the rosters into free agency, advance another day, don't schedule a fantasy draft, but opt for the new Free Agency Draft and with contracts already established, it'd be a bit different than the Inaugural where every demand IS a contract. You can still focus on minimums or near minimums for your own team, if you'd like. In fact, just talking about it makes me think about giving it a try just to see how it'd work.
The problem with the Inaugural, IMO, and I've logged it as a concern, is that the AI just doesn't seem to get that these draftees' demands are Major League contracts and tend to pile up on them because they have the money. The easiest workaround is to physically reduce the initial draft budget so no team has a great possibility of being able to spend 60 minimum dollar contacts, then consequently waive a bunch of players to get them off the 40-man, and have monies tied up in the minors with contracts that will be at least a year before expiring. Ah, starting to detour from the OP, so I'll stop at that.
As to negotiating the minimums, the all minimum league would be interesting and if you really wanted to personalize it- as suggested above by kingcharles -you could just offer extensions or editor adjust through your own method of design, e.g. offering the extension, gauging the amount desired, and modifying the existing contract.
