Mark, I am not sure what to recommend, but I think you actually don't want
Picatinny, but rather a
Weaver style (single) rail to mount various scope rings to scope. And you will need to choose the rail
and rings to match up together for best performance.
This may only be semantics, but should help in your search.
I do believe you are on the right track to get a single Weaver rail for a scope mount, for solidity and ease of good mount (without having to true up both fore and aft individual mounts), and more flexibility of mount. It will add a bit of weight (overall), but that can only be good for that cannon.
I have found the SWFA website to be the single most complete site on the planet for information about all optics and mounts (although sometimes I had to go to the individual manufacturer's websites to get particular details like weight, length, eye relief, yada on scopes I was narrowing in on). But then I kept coming back to SWFA for my comparisons. And, SWFA (I think) still has a price match deal, and when I found things a bit cheaper elsewhere, I still bought from them (with price match) so I had their rock solid reputation for defects or returns (instead of dealing with some one- off hardware store in New Hampshire running the closeout with the cheaper price). You just need to be able to fire them a link to the cheaper price website, to get the match.
https://swfa.com/There is some pretty good knowledge on here (mine is mostly about M1A(14) and ARs, but not traditional bolt rifles), but if no one comes back with what you want, I would consider getting on the telephone and calling SWFA or Brownell's (or maybe Midway last), and asking for tech support, specifically for advice on mounting optics on bolt guns. I've had good success with calling all three for personal advice over the phone. The folks I talked to knew what they were doing, and were never in a hurry, and very knowledgeable. Calling 2 or 3 of them might be well worth your time, before making up your mind. (take notes, and cross check advice between each outfit)
Besides any other long range shooters forums (I have none to recommend, but they are out there), you might also peruse AR15.com, but you have to navigate around looking for bolt guns (and not ARs).
The only other point I can make, is that I never like my scopes to extend even as far back as yours already is (I like mine mounted no farther back than even with the back of the receiver, if not farther forward, and with long eye relief, and I am a small 5'9 guy; but when I go for a tight check mount, unless the stock was too long for me, I'd get scope eye from a big 300WinMag, even as far back as yours is now. But everyone is different, just like bike seats.
The last thing to consider would be whether you might want some sort of lace on cheek pad for the stock to supply more support for a scope mounted farther back than what you now have.
That's all I got.