What are some alternatives for a glass stove top replacement?
Tempered glass is almost impossible to cut without shattering it after it's tempered, so you'd have to find a piece exactly the right size.  And even then I don't know if it would withstand high temperatures -- in fact it may get hot enough to un-temper it, in which case it would be a lot weaker and likely to break in normal use.

I have no idea if you can cook straight on the burners, but my guess is that since they're normally covered by ceramic glass, they're not constructed to support much weight.  Also I suspect they get a lot hotter than the glass surface does on a non-broken cooktop, so you'd be looking at an increased risk of fire if something spilled over.

I did a quick search and found a few online used appliance part suppliers, but I didn't check to see if any had that part available and at what price.  You might also call a few local appliance shops to see if they have any ideas on used parts.

A nationwide Craigslist search turns up many instances of that model stove for sale, all at prices lower than your price for a new part.  Sadly your most cost-effective option  may be to toss this one and buy a used one.