I have my 375 Allen Xpress which is very similiar to what your discribing and it is a great round. Much better then the 378 Wby and will do anything the big Wby will do and at times more and do it with less powder, less expensive brass and far superior brass in quality and stength.
500-600 yards will be easily doable, greatly depends on the rifle and how it shoots of course. The Ruger #1 can have its issues for real precision but sometimes they really shoot well.
You may want to try to get some of the new 350 gr SMK if you can in 375 cal. The velocity will be lower then your listing but the BC in the .77 range will give you alot more punch down range.
From what I have seen testing the 375 AX against similiar rounds like the 378 Wby and 375-416 Imp, the Lapua based rounds will do anything the much larger Wby or Rigby based rounds will do and again, often more because of the much stronger case. I think you would be very frustrated with the Rigby case as they are not designed to handle true modern high pressure loads for repeated firings. I always hear the arguement that the 416 Rigby can be loaded to match the 416 Wby in performance, that being a 400 gr at 2700 fps. That is true, then I ask them how many firings they are getting from their $3 each brass at those levels........
The Lapua will take more pressure and last longer hands down, plus its designed for precision, your on the right track.
Remember to post pics when you get her done and let us know how she shoots!!!