Turns out there is one person that Pete Rose could have bet with.
His employer. Baseball players and managers often pay them more if they win more games. Indeed, the Reds could enter into a Pete Rose memorial contract with a current player that exactly replicates the size of bets that Rose actually made in the past.
If fact betting through a bookie (or an insurance company has one great advantage over the current employment incentives. Under the current set up, the team is betting against itself at least with regard to this contract... and there are some famous examples where the team wouldn't let a pitcher start late in the season to preclude the chance of having to pay a hefty bonus.
It might be better if the team paid a bookie ... I mean insurance company a lump sum in advance to fund the bet .. then the team doesn't have any reduced incentive to win games.
Of course, bets with bookies aren't usually public... but mandating public insurance to fund incentive deals might be a better way to insure the integrity of the game.... and let gamblers enjoy the thrill of gambling to boot.
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Maybe it would be better to "bet" the way actors bet by winning a percentage of the profit. Then it seems more like a commission than a huge gambling-like pay-off. The manager and the pitcher would both have an incentive to win/play well.
Also, the current system is based only on winning, not on other factors that increase a team's popularity and profitability. In a commission style scheme, the players might try to prevent the kind of action which causes bad publicity. They also might try to reach out to fans more.