Let Plurality be the base-method. Partly because traditionalists can't object to it, because it's official now, partly because reform advocates uniformly dislike it, and so there's no favoritism. But also partly because it lends itself to the role.
Each voter has a Plurality vote. He/she can give it outright to a candidate, just as now. Or, he/she has the option to vote the voter's choice way. Voters may vote a ranking of the candidates or alternatives, and may declare a "designated count rule". Though obviously the election computer can't be programmed for every count rule that anyone could designate, it could be programmed to deal with a good number of the proposals that have some advocacy.
When designating a count rule, the voter is saying that he/she wants his/her Plurality vote to go to the winner produced by the set of rankings, when counted by that voter's designated count rule.
If you believe that a particular count rule is the best, you probably believe that it does a good job of picking the best candidate you can get, automatically compromising for you just enough. Well then, if you've chosen your designated count rule well, it will do just that.
So, your Plurality vote is guided by whatever count rule you want it to be guided by. Even though your designated rule isn't the official rule, it enables an optimally-placed Plurality vote. Remarkably, it's as if each voter can choose the election's voting system for himself. (admittedly, you can't keep other voters from choosing count rules that will do unwise things with _their_ Plurality votes, but those voters will have personal private incentive to pick a good one too.
I don't suggest Voter's Choice as the proposal to make when proposing single-winner reform. At first I'd try a proposal of a particular method, such as Approval, PC, or SSD. But if there's a degree of count-rule contention that is preventing reform, then I certainly would suggest proposing Voter's Choice, where everyone can choose their own count rule.