So I am at a point where my supplies should last me for the rest of my functional shooting life. I would like to pick up one more rifle for hunting purposes ( deer/moose). What I would like is a good bolt action chambered in something that fits the following:
1) Non magnum ( tired of looking for primers)
2) Reasonably tolerable recoil ( I am still pretty sturdy )
3) Relatively flat shooting out to 300 ish yards
4) No overbore cartridges
5) Larger than 30 cal
My current idea is looking at a 35 Whelen build but would like to hear some other suggestions and experiences.
I THINK I just did something similar to what you're contemplating as a last rifle. Bill Leeper keeps musing he's almost done gunsmithing every time I stop in to BS for a bit, and as he's started playing around making stocks, I asked him to make me a Mannlicher stocked rifle on a Husqvarna Husky action. Scrounged up a steel Mauser trigger guard/base plate to replace the alloy one and then waited patiently for Bill to finish the rifle. After 40 years of whacking moose, elk, deer and whatever with either a 30-06 or a 358 Norma Magnum, I opted to have it chambered in 35 Whelen. The short little Mannlicher stock and barrel and light weight make it a delight to carry out hunting.
It was more about the classic stylings of the rifle more than a caliber, but after watching more than a few bang/flops with the Thor's Hammer (another lightweight Husky), I wasn't too concerned that the same caliber of bullet moving a bit slower was going to disappoint. First trial load with the Barnes 200 gr. TTSX to get the rifle sighted in and out hunting before the season was over put 5 rounds into about 1". Sights adjusted, confirmed, load development complete. If I'm going to be in the alders hunting again where the local grumbly bears tend to be, I'll have something 250 grain up the pipe.
I have a real love for .35 caliber bullets as a reloader as they have a versatility I don't believe anything else can match.
Bulk pistol bullets and a few grains of powder allow you to heavy up for the bull gophers out there hiding behind their mounds, allowing you to shoot a 35 all day recreationally with minimal impact on your wallet, shoulder, or barrel. Further down that road, there are a large range of bullet moulds for 35s, although the one I have for this 35 is a custom mould for powder coating made to my specifications by Accurate Moulds - he does phenomenal work.
I even put together shot loads with Speer shot capsules for quietly assassinating grouse at close ranges while out hunting; the patterns look a bit messy on paper, but at close ranges with #9 shot they work. I do things like that when it's winter and I have too much time on my hands.
And as far as hunting bullets for deer to elk/moose goes, there's everything from lightweight to heavyweight bullets available: your choice. My wife has been wacking everything from antelope in Montana to moose up near Quesnel with the Barnes original 180 grain TSX to the newer model 180 grain TTSX with a Browning BLR rebarelled to 358 Winchester for years - also another tackdriver built by Bill Leeper.
If I didn't have three 30/06 rifles already, my last rifle would be a 30/06. It will do what you say you're looking for - other than your requirement to be larger than 30 caliber. It is a caliber that can justify its spot in anyone's gun safe.
Again, if it were me, it would still be more about choice of the rifle and style than whatever caliber you chamber it in.