Thanks. Passion Press is actually her clap, what I believe you're referring to is her j.down MP, which is her divebomb. I've gotten scared of using it because of previous matches I've had against him, but maybe I should use it a bit more.
These, particularly, stick with me:
I've gotten better at just walking when I need to, but all that changes in that Dhalsim MU. I guess it's his range that scares me. Thinking about there not being much push back, I need to be way more patient than I usually am, but in a way where I'm also advancing and not just sitting across the screen doing nothing.
Better whiff punishes is good, but I hate doing that against Dhalsim. Maybe I'm just not used to it; will have to practice that more in Training mode.
EX Shooting Peach can work, but I personally find it tremendously risky (I did try it once in that set, poorly, and got punished for it). I guess it's the quick reaction that requires when Mika is close enough to Dhalsim to actually punish what he's doing. If he gets too comfortable throwing out attacks too much, it's something I should keep in mind.
I went for the cut-and-dry explanations to give you a general concept to work with, so you can start practicing with a clear goal in mind, but as per always against skilled players it's always a matter of using those kind of counter-measures within moderation due to (which you already outlined) their potential to adapt. That said, I'll explain the type of mindset you need to carry over to the match-up in a broader sense.
Some of the points I mentioned in the list admittedly come with strings attached; it's a necessary concession you need to make to establish a certain pace or to send specific messages that a Dhalsim at that level needs to consider in the long run. The reason why he kept you at bay as handily as he did is simple from my point-of-view, namely your rhythm when attempting to turn the fight around being too... constant for your own good. That kind of aggression in itself isn't necessarily a
bad strategy when you choose your moments after examining his habits or conditioning him to how you would want him to respond in x or y situation, but you never really paved the way like that for future pay-offs. You would wait for a relatively long time without walking forward, and then if you decided to be assertive, it'd be repeated attempts to hastily crack his shell for a given duration until you went back to an (overly) defensive stance. It's a dead giveaway to any knowledgeable Dhalsim that their opponent is well out of their comfort zone, and often times they don't really need to contemplate on the possibility of signs of aggression being deliberately off cue even if it's as subtle as a second-long delay, which in turn could lead to big damage if (for example) it's a good jump-in. You immediately exhibited prudence without much in the way of a long-term gameplan against Dhalsim, whereas he
did make those minor adaptations to his patterns all the time to either land many stray hits to gradually whittle you down or to briefly anticipate your overzealousness.
It's easy to feel intimidated in that kind of scenario, hence why occasionally (but not too frequently) you need to set in stone that you can in fact hit him back at certain ranges if a Dhalsim player overextends. Even if it's just a stray Crush Counter from afar, that'll not only give you the one opening you need if he's already nearing the corner before he can retaliate, but it's another layer to your playstyle he'll have to consider if he sees you steadily fishing for it at 'random' intervals. Which in turn could lead to slight hesitations as to when to throw out limbs the next time, which could give you more time to slowly inch forwards, et cetera. Equally as important to bring up:
Dhalsim's grounded game is not that strong, unlike his ability to control the aerial space. His long-range limbs can easily leave him vulnerable if you predict them correctly, the pushback (as already mentioned) is fairly minor at far distances and his damage isn't particularly high either within the mid-screen space, meaning you can afford to take a chance. If you periodically use EX Flying Peach, he might be compelled to consider EX Yoga Fire / jab jab EX Yoga Flame (on block) in return, which then of course means his only 'burst' combo with his Critical Art is out of the question and subsequently opens up another window to potentially capitalize on. Sporadically back off (slightly at that) or simply sit down in front of him once you're past that hump to bait him, since his up-close-and-personal buttons (while serviceable) don't
excel at footsies - perhaps opening him up to shimmies - and maybe he'll flinch somehow due to the looming threats.
That's how you need to think ahead.
Bottom line: the calculated risks are a means to end to force a good Dhalsim to think more if you're successful to any degree. Learn what the preferable ranges are for whiff punishes / stuffing his limbs, when you could theoretically jump over them + land Mika's HK afterwards, be more irregular with your button presses or when you walk forwards -> block / opt for shimmies and so forth. It's an incredibly nuanced strategy quite frankly which will take some time to pick up on, but it's mandatory if you want to fight him in the neutral or outside the area where Mika can put people in the blender. The Mika mix-ups were, to put it bluntly, all you had going for you in that grand finals set vs Snafoo.