I think there's a very good argument for just shoving. It does make your hand look a lot like AK and may invite a call from TT+ Even if you raise to say 4K I really don't think you are increasing the chances of getting action from those hands. If anything I think you lessen your chances of getting called by making a pot sized raise.
Put your self in the openers spot with JJ if you shove. It's really tough to lay JJ, or QQ down but If you make a standard reraise I think I would make a standard fold. in his position, but if you shove I probably cry. And since you are increasing your stack by nearly 40% every time there is no showdown the shove is in no way an overbet and you're still pretty happy.
We are after more than the openers pathetic chipstack here.
Even if the opener calls and get lucky if u've brought another fish along for the ride there's a nice sidepot to win.