You're in luck here in that this is just with the edge board, it would be worse if it were one of the joints somewhere in the middle. It's hard to be sure from just the one pic but it does look like a couple of the other joints aren't great either which is sort of to be expected, but lots of not-very-good glue joints1 give decent enough service so this could be no problem.
Do I simply try to pour more glue into the cracks, clamp is again, and hope for the best?
Obviously you know this would be a ghetto fix and anyway this won't work. The existing dry glue in the gap will physically hold the two surfaces apart and prevent a good glue joint from subsequently forming.
Do I try to drip denatured alcohol into the cracks, to soften the glue and pry it apart, then try to glue it up again?
This is a reasonable idea but DA is the wrong solvent.
So, what to do now?
As bad as this looks and as weak as it will be (relatively) you may be able to get away with it depending on what this is for.
If you really want to get this off you can take advantage of this being a weak joint and just prise the two pieces apart. One or two flat-head screwdrivers or a couple of hardwood wedges would probably do the trick without too much difficulty. Bear in mind the amount of effort needed to get a lot of dried glue off the edges once you do separate them, this can take a lot more work than you anticipate if you don't have the right tools on hand.
So if you end up just leaving it you have a good number of options for filling the crack. If it's only visible on the underside I'd just ignore it, nobody else will know it's there and out of sight you'll probably forget about it yourself eventually.
For next time
- Work in subassemblies if you can't get this many glue joints done quickly enough.
- Have everything ready to go before even uncapping the glue. This should include having the clamps, at least the major ones, lined up and opened to the appropriate width for the glue-up being done.
- Work out a way to spread your glue faster2.
- More clamps or stronger clamps, and tightened harder.
1 Arguably the majority of glue joints done by weekend warriors and leisure woodworkers aren't as strong as they could be due to two factors. The first is because of the widespread, but largely mistaken, belief that clamping too hard can lead to starved joints. The second is that PVA is the most widespread glue used in woodworking and this requires high clamp pressure to achieve a strong joint!
2 Rollers are good. A notched plastic spreader can work well too, old credit cards or store debit cards are great candidates for conversion to spreaders (useful for both glue and some finishes).