I have done many 6.5mm wildcats, none have been larger than a RUM case.
I understand you don't want a Weatherby case, but it's hard to beat the 6.5-300 Weatherby for what you want…
The efficiency of the 300WM case is second to none, it is an excellent choice for 6.5/7mm, but, you are much better off using the dimensions of the A191 chamber when designing your reamer. I did this on my custom 264WM, it is magnificent at keeping the brass tight in the chamber after fireforming the shoulder.
What I found with both the 6.5mm and 7mm using a 7RUM as the basis, was extreme throat erosion, barrels lasted 600 rounds with excellent accuracy, beyond this, fliers got worse and worse and at 800 rounds, the barrels were toast. Both Stainless 416R barrels.
When I developed my wildcats on 416 Rigby Improved cases, the thought of doing a 6.5mm or 7mm had me wondering how many rounds I would get running 120g+ loads, my guess was 400 with good accuracy and done at 500.
The NMI is probably going to burn barrels like the RUM case does, albeit slower with a 40° shoulder, it will still be a 600 round venture.
Cheers.