I don't think you should be very excited about putting all your money in on this flop at all.  If you get 360 bb's in on this flop, you're pretty likely to be in bad shape, or flipping at best.  And flipping at an SPR of 9.4 isn't really how you make money in PLO.

So since you don't want to get it in on the flop, I'd suggest not raising either.  Raising would basically be for protection, but you'd be paying WAY too much for protection if you get reraised.  So just avoid trouble and call the flop imo.

jonna, so you would be flatting flop, flatting turn, decide river?

Well, you have discovered a weakness in his game, and you've now flopped a hand that you can use to potentially make his life very miserable.  Raising the flop isn't bad obviously, since you're probably way ahead of his leading range.  The thing is though, that with position, you're the one deciding how big a pot the two (or three) of you will play.  By flatting, you can keep the pot small on bad board runouts (such as this one) and can consider things like hero calling the river (though probably not a good idea).  On a better board runout, you can still easily get stacks in by the river if you want, whether for value or as a bluff.  You also avoid disaster the times that you do run into his monster hands.

On this board runout, flatting flop, flatting turn and folding river seems like the best line.  On some other board runouts I would be raising turn or river fairly wide.  It's just extremely difficult for him to do much about it.

With a higher SPR there would be more reason to raise the flop, but here's it's just not really necessary imo.  He also doesn't seem like the type of player to shut down when you hit, so I don't think you'd be losing action on your outs.