My guess is that they will not install a brand new engine but a used or rebuilt one. Make sure you confirm with them.What likely happened was the Cross-Over Coolant Pipe that is located atop of the intake but underneath the supercharger bursts completely. It's a known design flaw on an otherwise strongly build engine. That is the first place I'd expect to find a coolant leak that isn't visible because it "cooks-off" when it's a smaller leak. Upon complete failure what happens is exactly what happened to you...
New engine, $40,000... Let that loser Dealership totally replace that engine. They lied to you several times so let them pay for their moral bankruptcy! Also request they pay the monthly note until they get it 100% back to you.