[tmcdmck]

just to make things clear, by push you do mean bet pot right? anyway
the issue really revolves around what portion of his range you give to flushdraw, and what portion you give to straightdraw. i have no idea why you specifically weight his range towards flushdraw: could you expand on that? anyway: there is loads of maths, and a couple of read dependant points
1) does villain call turn with a flushdraw? if so bet turn all day long: considering your redraws the money you get from them calling with a flushdraw/ you filling up more than makes up for that which you lose to a straight
2) if not here is the maths:

at the start of the turn there is $27 in the pot. when you bet and they have a flushdraw, you win a $27 pot for $13.5 profit. if they have a straight you have 23% equity. presumabley they will shove, meaning you have to call $27.69, which you would actually require 25% equity to correctly do so. but, we will just assume there is enough random crap in their range to make you pot committed (lower sets every now and then, a flush draw they decide to play this way despite the fact they almost always fold it. i know this is unlikely, but it only has to be very occasional). for the sake of argument lets say you have exactly 25% equity vs their range. therefore when they have a straight you lose on average 3/4 of your money you put in on the turn ($41) and gain 1/4 of the money already in the pot (6.75), meaning you lose $34.25

therefore you win $13.5 when they have a flush draw, and lose $34.1 when they have a straight by potting the turn. if i am not mistaken that means they have to have a straight 28% of the time or less for potting the turn to be profitable, which is possible, though i reckon they have one a bit more, idk, depends on read. but, combined with the fact that they might suck enough to call with a flushdraw, potting the turn could well be +ev, though never by much unless villain calls with all sorts of crap we havent even considered.

BUT i doubt it is optimal. betting smaller would definitely skew the numbers in your favour (although it would not pot commit you leading to some really hard decisions on the turn, which it might be worth potting the turn to avoid). check shoving would increase the % of their range which was a flush, and they would NOT be pot commited to a call when you shoved, meaning you would win a $81 pot from them when they had a fd rather than a $27 one. But you would risk them checking behind and getting a free card with a fd. i cannot be bothered to do maths for this right now :P

anyway, i never play omaha, so take my advice with a pinch of salt. I also am a bit of a noob at poker maths, so i might have gotten something terribley wrong. but basically: potting turn is read dependant, butif wrong, it is never that wrong. if they are aggressive and will usually pot the turn if checked to a check shove is MUCH better.