I can do 300W for 30mins - does that mean I can barely heat up a Pop-Tart?

Spend 30 minutes charging a battery and you should have enough energy to turn any flavour of pop-tart into carbon flavour.

Even without a battery, I could easily imagine designing an efficient single slice toaster that could handily brown a pop tart on a 300W budget.

You wouldn't need any sort of fancy toaster: anything small, rated >= 300W, would deliver cyclingpower from a rider of any skill.

That actually could toast a few batches of Pop-Tarts.

If you like then "golden," perhaps the entire box.