[06/16/2019 @ 7:40 PM CT] Updated post. Still available.
British Airways and Delta have round-trip flights from Austin (AUS) to Prague (PRG) for $631-$635 with a connection. Flights October to March. Departures on Tuesday and Wednesday. 7-day minimum stay required.
Note: Carry-on bag is allowed for free on British Airways and Delta. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.