Ok you asked for it...but I will be kind.

Seems to me if you don't trust the shop then they shouldn't be doing the work on your car. In fact if I don't trust the shop they don't keep my car overnight let alone for the amount of time it takes for a swap.

Grab your engine and your car and bring them home and do the swap yourself with a few friends and some beer. The H swap is actually really easy to do, I was pissed the first time I did one and realized how easy they were. If I had known that I would have done the swap into my accord myself.