Im also late to this thread, and while I think that leading out is better, I doubt much would have changed. As NL said, you maybe would have gotten a couple bucks more. Also, it's good that it turned out the way it did with all the money going in before the river, because that T could have killed action. Chuck I'm not sure why your thinking you could have gotten more value, maybe you mean that your raise to $35 was too big for MP to call?
Things could have gone worse in this hand when you think about it. For the sake of it, lets say you lead out for $7, MP calls and CO raises to $20. What do you do now? The big problem now is that you might raise again, but you might also be tempted to just call the raise in an attempt to get a call from MP, who might just fold anyway. As it turns out, this could have cost you some because that river is an action killer. You'd have $42 left, so at best you can lead out again on the river for $20, and if only CO calls your bet it turns out you actually made $7.50 less. That's just one scenario, I can come up with others where you lose even more than $7.50, all because you're trying to get action from MP.
This is results oriented of course, but nevertheless it all applies, because when board has a straight and flush draw like in our case there always is the chance that an action killer card comes on the river just because there are so many of them, up to 13 in this hand and that's not counting the board pairing, so it's best to get as much in the pot as possible.
One more thing. Lets say you check/raise less than $24, specifically rather than making it $35 to go you make it $22. I don't think much changes from MP's perspective, because it's still a raise and reraise after his bet, so unless he has a strong hand, like a set or a big double draw, he just has to fold because of the threat that CO could raise again. Even hands like top 2 pair are forced to fold there, because they're clearly behind and with little chance to improve. However you look at it, MP is faced with a triple danger, which are a raise, a reraise and the chance CO raises again, with the latter being the biggest threat, so only a very strong hand can hang in there unless he's a donk (there always is that chance though, nothing bad in being optimistic, right ?).
Seriously, I think you got the most out of this. Without being results oriented, I prefer leading out because of the chance it gets checked around. If that happens, your hopes of playing for a big pot end right there. I know you said that CO was aggressive, but the fact he's in position in a limped pot can mean he called that flop bet and raise with a huge variety of hands, and not all of them might bet the turn. MP looks like he has a hand because he raised your flop bet, but as was said it could simply be some kind of A9 hand since it's a limped pot, and the fact his raise was called by both of you + the turn bringing an overcard might slow him down. Going for the check/raise has some merits, but bottom line is that, IMO, leading out is the better play because it gives you the greatest chance of playing for a big pot, which ultimately is what you want.