Unless you plan to buy used I don't think you are going to find much of an upgrade from the axis for $400 especially limiting yourself to .270. Most of the best deals on new rifles are .223 or .308. $400-600 can buy you a lot of Savage if you don't limit yourself to .270. Also with that budget for a deer rifle. I would get spend 100 on tasco and decent rings and put 500 on the rifle.
Sticking to only the models I know 4-600$ can buy
12fv
11 hog hunter
10t
10fcp-sr
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