Legacy Keyed Handle Set 3-15/16" (1-1/8" to 2-1/2")

There is no mortise you can install on your door that would get the Legacy handle set to work. Your door is a completely different kind of door that is incompatible with the hardware you purchased.

It looks to me that your door once used something like our 82-002 or 82-008, but that's just an educated guess. I won't be able to say for sure unless I can see the original handle set. Do you have it on hand?

Yep, that looks like a match for our 82-008. I'm afraid you're stuck using this lockset. This type of door isn't designed to use anything else, and getting substitutes to work never pans out because of that huge rectangular hole. 

Between you and me, I hate this kind of door, but they're super common. Concerning your issue with the door thickness, I have heard of that before. In my experience it could be worked around by using longer installation screws and packing out the lock "tooth" with some washers. See if that could work for you.

That is a little thick. It may work okay, but in a worst case scenario you'd have to reuse your old screws and maybe pack out the latch hook with a washer to get the clearance you need.