I'm having a hard time keeping my spikes up. I'd estimate they're about 2-2.5" at their highest, but I'm having trouble applying the glue.

I towel my hair off once when I get out of the shower, and then with a smaller towel after I get dressed, but it seems that even then the hair's too heavy from the water, because it seems that no matter how little product I use, it slumps back over as if I never put anything in it. If I put more in, my hair gets oversaturated with the product and weighed down. (i.e, I get the spike, but it just droops and sits on my scalp instead of pointing up.)

I tried waiting until my hair was pretty much air-dried, but I have some moderate waves in my hair, and using wax or glue on completely dried hair is difficult, since it doesn't smoothly form spikes like it does when when wet. I end up using so much cream and glue to achieve that smoothness that it just ends up too heavy again. But if I don't do that, the hair just becomes a mess, it doesn't form a spike until I use "too much" product and becomes too heavy.

Any advice (that doesn't involve straightening irons? Blow-drying and straightening just bakes my hair, no matter how much safety product I put in before.)

What products are you using?

I've been using various the following products on their own and in combinations with each other:

Got 2b glued glue
Got 2b glues hairspray
Brand I can't recall Matte Wax
Matrix Biolage Wax-Cream
Rusk Wired Flexible Styling Cream (this stuff worked great when my hair was shorter, but I don't really like it that short... was kind of a faux pas on the stylist's part)

Maybe you're using too much product at once.
I've used Got2B glue and that stuff is heavy.
Even on my friend's short hair I was having trouble.
So you have to be careful and not use too much.
I haven't spiked hair in years though, so you might want to check out this article for more info.
http://haircrazy.info/stylingguides/spiking/

I think the question I'm having the hardest time figuring out, though, is how wet should my hair be when completely dry isn't cutting the mustard?

I'd always make sure the hair was slightly damp because too much or too little moisture would make it impossible to work with.

So a thorough toweling should do the job?

Yeah that's pretty ideal, but if you find it's still too heavy I'd let it dry a bit more.

Water will add a lot of weight so get it as dry as you can. Did you consider blow-drying it straight?

Another option is to have your hair thinned a bit using thinning sheers or razoring the ends. That will take a lot of the weight out of it.