Tim, welcome to Marlin Owners.
Your quest for the ultimate woods rifle is equivalent to opening a can of worms around a campfire. You are going to get varied answers in varying calibers.
To better answer your question between the three rifles cartridges, what range of shots are you looking at? Then we can better match what caliber in a Marlin platform to your range of hunting.
That said, the 338ME is the most versatile cartridge out of the three you mentioned. It delivers the most energy on game in the widest range of hunting and at quite mild recoil. Below is a recoil table for 308ME, 338ME, 45-70, and I threw in 444 Marlin for possible consideration depending upon your hunting range.
Cartridge/bullet weight/velocity--rifle weight--recoil energy--recoil velocity
.308 Marlin Express (160 at 2660) | 8.0 | 13.4 | 10.4 |
.338 Marlin Express (200 at 2400) | 8.0 | 16.2 | 11.4 |
.338 Marlin Express (200 at 2600) | 8.0 | 22.0 | 14.0 |
.444 Marlin (240 at 2400) | 7.5 | 23.3 | 14.2 |
.444 Marlin (265 at 2200) | 8.5 | 22.1 | 12.9 |
.45-70 (300 at 1800) | 7.0 | 23.9 | 14.8 |
.45-70 (350 at 1900) | 7.0 | 37.9 | 18.7 |
.45-70 (405 at 1330) | 7.5 | 18.7 | 12.7 |
The 338ME lists two velocities which are depicting an MX and a XLR. The MX velocity listed is too low, should be @2500FPS but you can see the difference two inches in barrel length. I own both the 308MX and 338MX and both are very mild recoil, in fact, I don't notice all that much difference between the two.
I threw in the 444Marlin as a consideration along with the 45-70. The mighty triple four is hard to beat out to 200YDS but the 338ME still delivers more energy on game.
I have spoken to Hornady many times regarding the ME cartridge. They will never orphan us by discontinuing these cartridges. They have a reputation for keeping their word. And if you reload you wouldn't need to worry anyway.
I have spoken to Marlin many times and they have indicated several times the Marlin 308MX is their most popular selling rifle. Though, this was during the 338ME's suspended production while they retool. The 338ME rifles are currently in production so in time we'll see how the 338ME sales stack up to the 308ME.
You mentioned a shorter barrel to pack in the woods. I've hunted Elk for over 3 decades and a 22 inch barreled lever action rifle packs well. Both 308MX and 338MX sport a 22 inch barrel. Yet, it is a personal choice.
Regarding ballistics and terminal performance, the big bores range is much shorter than the ME cartridges but are quite capable within their respective range. The 338ME has the broadest range delivering the most terminal energy and flattest trajectory of the cartridges you mentioned. It is capable of taking Elk out to 400YDS should the need ever arise.
I'm planning to purchase another 338ME in an XLR stainless. I will cut the barrel to 22 inches and re-crown. Then bead blast the SS to a satin finish. I probably will have the Nib-X finish added to make it an all weather rifle.
I'm currently developing premium bullet offerings for the 308ME and 338ME cartridges. They will be bonded and offered in varying grains of weight for those who reload. We are getting close to wrapping up the 308ME bullet offerings. Further, these bullets are specifically designed to the ME cartridge dimensions which will be a first, offering premium bonded bullets for the ME cartridges.
So, there you have it. If you get into reloading the ME cartridge of your choice you'll never have to worry about ammo availability.
I hope this helps
Jack