Oh you poor [censored].
I owned and maintained a '94 Corsica for just over a decade... I'll just say it was an interesting experience- culminating in the sudden and unceremonious death of the transmission about 700 miles from home a few weeks ago (at 182,000 miles). But I learned quite a bit along the way, and became quite the contortionist... a skill that you'll be familiar with if you're replacing the heater core on one of these.
I replaced the heater core on mine twice over the years. I had a GM factory manual, and as I recall... to do this job by the book, you have to REMOVE the center console, then take the carpet loose and pull it back out of the way. Don't remember exactly what other steps were laid out; suffice to say that I wasn't ABOUT to do all that.
The way I removed this thing is pretty similar to what you're doing. I removed all the screws in the heater core box. I don't remember exactly how many there were, but I DO remember that there are a couple clear in the back that are very hard to find and remove... so make sure all the screws have been removed. Then I pulled up on the top cover and broke it- it was MY car, so I didn't care... and a crack in the plastic is a small price to pay for saving a full day's work IMO. That allowed enough clearance to get the thing out. Barely.
The heater hoses are just as much fun as the heater core, at least with the V6- don't know about the 4 cyl. You can access those heater hoses from the top by laying across the engine... from the bottom if you put the car on jack stands... or through the driver's side wheel well. None of these options are easy, and it helps if your arms hang down to your knees like mine do. Having changed the heater hoses once and the heater core twice, I've done all three. And given the choice, I'd probably bite the bullet, remove the driver's side front wheel, and reach in where the tie rod comes through.
I wish you the best of luck. I hope your health insurance is paid up and includes mental health benefits. Please make sure no women or children are within earshot whenever you work on your Corsica. And keep an eye on those intake gaskets.