Geni can only show paths that *HAVE* been established - not ones that exist only in your imagination.
You are making an unholy lot of ASS-umptions, starting with the ASS-umption that ALL Prices everywhere and everywhen *must* be kin to each other and to you.
This is not necessarily true, and it *is* where a lot of raw amateurs (including Emma Siggins White) go cuckoo for coconuts.
Your second bad ASS-umption is that there is *any* connection between John Rice of Dedham and *ANY* Welsh Rice, Price, Ap Rice, Aprice, or whatever.
He is probably not Welsh, but East Anglian, and you have gone barking up one wrong tree after another for years trying to find a connection that just isn't there. (To be blunt, you may *never know* who his parents were, and you will have to be satisfied with not knowing.)
The *very worst* of your bad ASS-umptions is that two men born twenty years apart, on opposite sides of the Irish Sea, *could possibly somehow* have been "the same man". No. Nohow. No way. Drop it. Forget it. You will *never* get *any* serious genealogist to accept such nonsense. If you publish that, you will be a laughingstock.
There is no "fear of putting Perrot ap Rice in his proper place". He *has* his proper place, and it's back in Wales. As for alleged "disapproval" of his "activities" in Puritan England - get real. *Most of us* have Puritan ancestors, and a lot of them went from England to New England so they could persecute each other (and everyone who disagreed with them) in relative peace. (Some of them went to Virginia and then hiked up to Maryland - I've got a few of those, and a lot of Quakers, so there. I've also got the chief Quaker-persecutor in Virginia history. So I don't know what that goes to show - probably, you can pick your nose but you can't pick your ancestors.)
What really rankles you, I bet, is that I've got a better claim on Perrot ap Rice than you do. I can actually show - and prove - a valid, if indirect, relationship: he married the sister of my 8th great-aunt's grandfather.