[joewatch]

I don't play at this level, but from what I know about shortstack play (which comes entirely from reading Rolf's articles) -

I think a reraise is a bad idea here because you are now basically pot committed with 35% of your stack. This is a great hand to play post-flop, but not as good to get it all-in preflop. You are a dog to kings, and even a bigger dog to aces:

pokenum -mc 500000 -o kh kd 7h 3s - ad qc js ts
Omaha Hi: 500000 sampled boards
cards win %win lose %lose tie %tie EV
3s Kd Kh 7h 265211 53.04 234789 46.96 0 0.00 0.530
Js Ts Qc Ad 234789 46.96 265211 53.04 0 0.00 0.470

pokenum -mc 500000 -o ah as 7h 3d - ad qc js ts
Omaha Hi: 500000 sampled boards
cards win %win lose %lose tie %tie EV
As 3d Ah 7h 322337 64.47 177663 35.53 0 0.00 0.645
Js Ts Qc Ad 177663 35.53 322337 64.47 0 0.00 0.355

Post-flop, the obvious play is to push it all-in to represent your aces like you did preflop. Check-call seems ridiculous.