Sat to $100k - What to do?

[TheDespot]

Middle of satellite - ~100/215 left, with 21 getting spots

Blinds T$50/100, no ante

Hero (T$2315) is button with Ad-Qd

UTG+1 (T$1955) limps, CO (T$1535) limps, SB has T$5500 and BB has T$2930. (I just got switched to this table so I have no reads whatsoever)

I'm mostly a cash game guy but I've been delving into some MTTs as of late so forgive me if this is a standard spot and I'm just a tourney donk for not realizing the obvious. Anyways, is a shove in order here? The problem is both limpers have awkward stack sizes and the blinds are pretty deep-stacked, so I wasn't sure exactly what the move is. Still, my hunch is a shove is best, but I'd like to hear some thoughts.

[ToX1C]

Raise preflop for 500.
Then reevaluate the Flop, if you get callers.

[bazooka87]

I think you're a little too deep to shove for just 350 chips, I like a raise to 500 as well

[TheDespot]

Okay, well I raised to 400, the blinds folded and one limper called.

Flop K-9-4 rainbow
Villain checks, Hero?