Well, I am pretty sure the plastic undertray will be completely liquified in seconds. You can probably kiss the lower radiator hose goodbye as well and if that melts, all hell breaks loose. There's probably a dozen other things that will be destroyed pretty quickly I am not even thinking about.
It's probably worth the $80 tow.
If you could get chummy with the shop owner, maybe he would let you install the downpipe at the shop. We probably all had our manifolds off enough times to do it in a reasonable amount of time, although I like to drain and remove the radiator to give myself more room to work, but not like you couldn't bring a couple gallons of coolant and distilled with you.