MP1 puts in nearly 1/3 of his stack and you think you can get him to fold AK, AQ or even 99-JJ. Be real.

#1, most people will go to war with AK.
#2, some people will go to war with AQ but possibly fold to major aggression, but with 1/3 of their stack out there, they are most likely going to war with that, hoping they are in a race.
#3, if i'm villain and have 99-JJ, put 1/3 of my stack in and you limp raise all-in, I'm praying you have AK or AQ and I call (of course i'll be ecstatic when you flip over your 88)

This was a bad play against a player who is getting close to desperate with his stack and has shown he is willing to go to war with his hand. Your best chance is a race. This was not a good move and UTG+1 was still to act when you pushed. Very risky considering the range of hands you put him on, he's not going to fold that range 90% of the time.