I am putting the finishing touches on my first AR and I am unable to mount both my scope and BUIS at the same time.  I have a standard A3 upper receiver with a Badger handguard and I am using ARMS 22 High rings, a Leupold MR/T, and a YHM rear flip up.  Any recommendations?  I have tried moving the scope as far forward as I can without exceeding the eye relief limitations and I still can't clear the sight.  I'd rather not have to buy a whole new set of mounts, but I am not sure that a spacer (i.e. ARMS 36) is the best solution, either.  In reality, I will never need the BUIS to save my life and I could keep it off the rifle until I want to use it.  I am just lazy and would prefer to not have to continually remove and replace the rear sight every time I switch back to shooting irons.  Thanks in advance.

The cheapest solution would be to get a riser of some sort. Personally, I like the YHM 5-inch rail extension.

I'd rather not have to buy a whole new set of mounts, but I am not sure that a spacer (i.e. ARMS 36) is the best solution, either. In reality, I will never need the BUIS to save my life and I could keep it off the rifle until I want to use it.

You answered your own question.
Or get a GG&G scout rail

Get one of the ARMS #38 sleeves, they are the originals and have the rear sight built into the rail. Then you only need to use med. ht. rings from then on.
Jack

Here's  a Yankee Hill handguard, LaRue tactical scope mount, Yankee Hill low profile BUIS.  IOR M2 scope