Handling "Upside-Down" IC Pinouts on PCB
The 80QFP is thin enough that you may be able to place it upside down on the board, glue it in place, then carefully bend each pin down to its corresponding pad, and solder it. 80 pins is a lot to do that for though, this method is more commonly used on smaller chips.
I'm trying to find a good picture showing this technique.
At least, that's what I would do, just about any other method involving bodge wire (such as gluing it upside down and using wire to bring the pins down to the pads) or adapters will be very cumbersome with a package that size.
While the procedure given by uint128_t is probably best, here's another.
Get yourself a spool of bare 30 gauge wire. Solder a short length to each pad, with each piece perpendicular to the row of pads. Now place the IC on its back, but use something like superglue or RTV to tack it in place. Now bend each wire 180 degrees and solder to the appropriate lead, and snip off the excess. Now use something like 5-minute epoxy to run a bead around the pad area, fixing the jumpers in place without shorting to each other.
uint128_t's idea is, as I say, probably best. With the chip in place (and tacking it down is a good idea), use a fine-tipped probe to bend each lead into position. Do this with a single, strong push and you are unlikely to fatigue the leads.
Either way, it's going to be a tedious process.