I would have made the 3Bet bigger and 5Bet jam.
Don't understand why you would like to play this hand with a 10K pot with both of you less than 9K left. He might push his (ex AJ) hand only if he hits top pair? Let him put it in pre, and you'll be good in the long run.
After all, why did you make your 3bet so small? To get his money in, right? Well, you should go ahead and think the same after the 4Bet then, en not just give him a change to outflop you with a worse hand imo