I don't know about the 208 Amax but you can stabilise a 185 Berger/Lapua Scenar, Sierra 190 & 200 HPBTMK in a 1:12 with a 300wm so I would expect to see a 208 work in a 1:11 and be a bit surprised if it didnt.
A lot of people use too much barrel twist.
For accuracy you want the slowest twist rate that gives stability.
If you find they wobble just drive them a bit faster and they will come good. Its only when you attain maximum available velocity with no result that its all over.
In attaining maximum velocity you will soon find that quality brass is worth the money.
The 208 may not stabilize all that well in the tikka with only the 1 in 11 twist. On the other hand the extra velocity might just get it over the line. I have a tikka in 30/06 and have not had a chance to load for it yet so am hoping I can go up to 200 grn woodleighs. As for the 223 in a 1 in 12 twist it will be fine up to 60 grainers
If you are using the 208 in your win mag, you won't have an issue. I can get 2960 fps with 73gr 2217. The barrel is a 1:11,
and I will soon be putting them through a 1:12.
Well for my Tikka I have found that 50grain nosler BTS shoot the best. But not far behind are the z/zmax 50gn. I went with the zmax for economy sake but have been happy their performance anyway. I have never shot heavier 55gn as I have only been shooting foxes etc. for SPs the nosler shots were good but 55gn Sierra super roos were really good I do like boat tail pills but I think that's because I find them easier to seat. Out of factory rounds, best I shot and best overall was American Eagle(federal) 50gn HP. I was shooting a LOT at the time but these things were shooting one holers day in day out. I think they were flay based but I am not sure now. Not sure who made the bullets but they were bloody good perfomers considering they were target projectiles. But at a buck a shot I was burning a lot of dollars back then.
I will not go below 50gn. One sample of 40gn hornady TAP bullets has put me off the lightweights! MASSIVE muzzle flash and the bloody things constantly splashed on the skins.