I think the three things that really changed how I view Painwheel vs. Parasoul matchup were the realization of how important Napalm Shot is to maintain her up close pressure, how good PB Absolute Guard and PBGC is for her fuzzy mixups while lockdown assists are present, and how straightforward Parasoul is, both in ground movement and jump arcs/hangtime.
First, if you pushblock her napalm shots at the end of blockstrings, it seriously messes with her jump-ins and you can breathe again. She's forced to dash at you to close the pushblock gap, and while she may get some quick strings if the spacing/timing is right, you can usually get a CH armored st.HP if she tried to follow up on the ground. So essentially, block the guard string to the best of your ability > pushblock shot > if jump-in, punish her whiff if possible; if ground dash followup, armor or jump/fly.
Secondly, for the corner pressure, I've seen very few Parasouls that don't use a really good lockdown assist to hold you down so they can present the low/high mixups, which means that if you use the lockdown assist as PB fodder to either try to PBGC deathcrawl your way out or absolute guard the scary low/high|high/low part of the pressure string. Cerecopter is really taken for granted as this amazing great lockdown assist right now, but I'm beginning to think it's more of a liability as it's active for so long it basically gives away a PBGC or PB Absolute Guard which is really self-defeating if you want to make them guess on a high/low mixup.
The third thing is that Parasoul's air moves are great because her air mobility is nonexistant. She's beaten me in air-to-air fights more than any other character, but I think I've dashed under jump-ins to cross-under her more than any other character. I've also probably air-thrown her more than any other character because she's not airdashing or double-jumping, which makes her jump arcs super easy to react to.
For fullscreen tear tosses and napalm shots, there's ways to maneuver such that it's extremely difficult for her to get any chip and you can just hang out indefinitely or try to close the gap. I'm actually going to have to draw a picture for this, so watch for the edit.
Edit:
Painwheel is the cute octopus.
Mary Poppins is the umbrella.
The red line is MP Shot, the Blue LP/HP.
The circles are areas where shots will either turn into static tears if blocked, or where tear tosses will generally fall.
You can fly in the space between the two shots' trajectory no problem. If you're in the trajectory of the MP shot while flying, use (1)j.LK, (2)j.LK, or (3)j.LK as a sort of budget unfly to get out of the way. If at any time you feel like you can't dodge one with maneuvering alone, you can start the j.HP and use its armor but flight cancel it before startup so you can get back to maneuvering. Hopefully to the nearest safe zone.
The goal for me is to get into the middle where there's no coverage, at which point most Parasouls will either call an assist to challenge you in that space, or dash and jump at you with j.LP, j.HP or an air throw. Once you're in the mid and see either of those starting to happen, you want to (1)j.LK to block the assist and put yourself right in front of where she'll land for whiffing those air buttons.