Exactly why I was asking for a $22k breakdown. The whole story just seems to not be there. I do not doubt that the OP is in a pickle but I just think there is more to this. Hell, I just found out that AAA is now involved. I would want a complete detailed explanation of what they are offering you for $22k. I recently was involved with my neighbor and replacing his engine with a crate Ford engine and a very reputable local transmission shop rebuild with all the new bells and whistles. The engine from the dealer was $5798 and with my military discount was $5218. It was for a 2006 F150 and is a 5.4. Retail pricing, in the shop, would have been near $8k to $8500, just for engine.
With the engine and transmission and all the additional new parts like radiator, condenser, accumulator, transmission cooler. lines, hoses, new throttle body, all 4 oxygen sensors, mounts, belts, tensioners, idlers, reman alternator, knock sensors, camshaft and crankshaft sensors, thermostat and housing, MAF, Cannister purge valve, fuel filter and regulator, water pump, injectors, fan clutch and blade and all fluids and labor, the bill was close to $17k.