Alternative Options

I would do what FEENIX mentioned and go with Hawkins Hunter DBM, if your stock is inletted for M5. I would go with a 6.5 PRC or change your bolt head and switch to a 6 mm Creedmoor, that is low enough recoil and with a brake should make it easier for you.

 
Target shooting or hunting? If hunting, what wild game and how far?
Both though I mainly target shoot with magnums. I hunt with a 300aac and 357 mag
What wild game and how far help determines sound advice/recommendation? I do want to speculate, but hunting with .300 AAC for me is close hunting, i.e., for deer and smaller games. The more pertinent information you provide, the better. If you are doing target shooting at 1000Y, you do not need the magnums you have and have mentioned, especially when you reload. LRH members here shoot targets beyond 1000Y with their .308 Wins.
 
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The zermatt bolt change is pretty cheap and easy. I've run 243 and 6.5 through my TL3 long action without any issues, that being said the spacer system looks pretty handy. The area419 brake is what I've gone too as my shoulder has deteriorated and it's made the biggest difference of the brakes I've tried on the magnums.
 
Now that I have some more info, I would swap bolts/heads and shoot something like a 6CM, 25CM, or 6.5CM for targets.

Very little reason to shoot magnums for targets. But if that is what you want to do:
6.5PRC
6.5SS
6.5SST
6.5SAUM
25PRC
25SST
25SS
25SAUM
6PRC
6SST

These will all work fine in a magnum long action. Lots of guys run that combo. My brother included. 6.5PRC feeds smooth as silk in his LA.
 
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