You type too much.
This seems like a far cry from posting on the league message board and pissing everyone off.
The most valuable "asset" in any fantasy football league is not money, it's good solid committed owners with an advanced skill set that competes relentlessly.
Most leagues have some committed owners, some wishy washy owners and some owners that are close to abandoning their teams. Obviously money leagues and how much money raises the stakes and raises the level of the kind of potential owner you get.
Good competitive leagues are always on the lookout for good owners. If you get a reputation as a skilled fair competitor with good communication habits and you have a habit of making your team consistently better, despite what you might have inherited to start, other owners notice and eventually will want you to join their other leagues.
If you suggest what you are suggesting, you will start closing many of those doors. Whether you feel that's fair or not.
I'm from the old school. I was playing fantasy football back when you had to get newspapers and look up box scores and mail in your lineups with an envelope and a stamp. I've seen enough and experienced enough kind of leagues and situations where I'd say if you want this kind of option, then the best course would be for you to start an entirely new league with this scenario as part of the actual league constitution.
If I had a choice between two potential owners in a fantasy league
1) A guy with extra cash and is willing to pay money to improve his odds by buying an improved draft slot or an entire roster
2) A guy who says, "You can put my into any situation, I can inherit any team, under any circumstance, under any limitation, and I'll still find a way to crawl inch by inch and punch you in the mouth"
Well, I'd pick the 2nd guy. But that's just me. Personally I sometimes enjoy inheriting a bad team, limited on draft picks by previous trades by the old owner, broken roster, looks a bit hopeless, then fight like mad to turn it all around. Organically. Like it was a personal grudge. I see a "bad starting draft position" as a challenge, not as a precursor to a transaction.
Start a new league with the rules and league constitution you want, if you want to pick something off the beaten path. Then everyone knows and agrees upfront on what they are getting into and risking their money on. I believe that's the best solution.