First, take a breath.
The worst case scenario is that you'll have to paint again. They're not a loss at all. You're freaking because you have a picture in your head that isn't happening. At least right now.

I am not a pro, but from all my reading I'd stop what you're doing.
Let them dry off.
Scrape (with a plastic scraper, not metal) anything loose off of them.
Then I'd take mineral spirits and wipe them down to neutralize anything still on the surface.

Then start reading. Your finishes are going to determine how well/fast the strippers work. First read the directions on the strippers you have, then in the woodworking forum, because all of this is covered about a gudzillion times.

The most important thing I learned is that 20 minutes of leaving the stripper on is a joke.

I'm assuming you've taken down your doors and taken the hardware off? If not, do it.
In a well ventilated area, lay your doors down and pour on the stripper. Mush it around until everything's covered. Thickly.

Either put these IN a black bag and seal it, or lay black plastic on it and wrap it tightly. Keep it in a warm place, but don't use heaters. Leave it for 45 minutes. Don't peek.

After about that long, lift up an edge and see if your plastic scraper will lift some of the paint off. I've found, ironically, it comes off the detail better than flat surfaces.

If it's not coming off, wrap it back up. If it's dried, scrape, then put more on and cover it tightly again.

Keep doing it. You can remove what you can each time, but if it's not coming off, don't use brute force. Just more stripper. I've found toothpicks work well for getting into detail.

For the cabinet faces if still on the wall, I cut thick strips of plastic, put the stripper on and taped it on with painter's tape. Make certain to put something down to protect your counters from drips. (Although I've learned that Wilsonart HD can withstand paint remover!)

Patience is your friend, although I hate that "p" word as much as I hate the "m" word (moderation).

Refinishing once the paint is off is a whole 'nother message board and I refer you back to Woodworking or Paint.
Most of all, since you've got a lot of time to kill, while you wait for the stripper to do its job, search and read.
You're not the first (I'm here to tell 'ya!) to learn from the expertise and experience on these boards, so avail yourself of their trial and errors, and professional advice. Read.

I have a bookcase to redo some day for the same reason. I do not care for BM paints - particularly the waterbourne satin impervo.

Try straight ammonia. Do a small test by pouring a little on and mopping it off after a few seconds. It'll be almost instant if its going to work. It only works sometimes, but if it does, you'll just need gloves, respirator (which you should be using with an paint stripper), eye protection and a sponge. You finish with a light sanding as prep for a new primer.

When you repaint, try using a premium enamel type paint - or a high acrylic content paint. Fine Paints of Europe is worth every penny for cabinets and woodwork. It really does self level, covers well and drys hard. Nothing sticks.

I don't think its a happening idea to poly over latex. There will be others who will disagree ;)

You said you used latex paint. Was it latex primer too?

You might not get every last bit off the cabinets with the stripper. Raw wood tends to have so many little fine crevices for it to get into. But once you have it down to almost bare wood you can sand off the rest.

I am using CitriStrip and am amazed at how well it is working. And like CEFreeman said, it takes much longer than the label says. I put on a thick coat of stripper and wait at least 30 minutes before even checking on it again. The nice thing about CitriStrip is that it turns the layer of varnish into dry, crumblies and is really easy to get most of it off.

If the carcasses are stripping well but the doors aren't, there are places that do dip stripping that can definitely get off the paint. In my kitchen, the carcasses are a breeze and the doors are more work.

Also try the paint forum. I think you need some professional advice and maybe even a professional to paint them. Here is a site that might be helpful be sure to click the before and after tab Link below:

Here is a link that might be useful: painting existing cabinets