I was able to get a Remy for 3:25pm around 3ish (guessing 3:02) while waiting in line to get into Epcot (IG). This was mid-March.Just catching up on this thread after my trip 3/31-4/10. I didn't see that anyone answered your question and wanted to tell you my experience: We stayed offsite I was able to book FOP, Rise, Remy and SDMT. Remy and FOP were available about an hour after park opening so I booked them even though I hadn't planned on it. Rise and SDMT initially appeared to be sold out but by repeatedly refreshing at park opening I was able to snag evening timeslots for both. Don't despair!
Edit to add: My HS and MK days ended up a 9 on Touringplans (were supposed to be 6s) and I still was successful!
We were onsite so that was my only experience trying after park open. Glad you were successful!