Plywood is generally 1/32" less than what we see marked as 3/8, 1/2, 5/8, 3/4 etc. Four pieces of 1/2" ply will get you 1-7/8", as you've found (4 x 1/2 = 2", then subtract 4 x 1/32"). If you want to hit 1-3/4" dead on, try three pieces of 1/2", plus a piece of 3/8" and you will be right there. I've spent way too much time pondering the same dilema and this is what I did on my last form - it is exactly 1-3/4" as close as can be measured. You will have the added expense of one sheet of 3/8 (with a lot of 3/8 left over for another project).
Two other combinations that will get you real close are three pieces of 5/8" ply (if you can find it), or two pieces of 3/4" and one piece of 3/8". I just glued one up in that combination and it is 1/32" over 1-3/4", so is just a little fat. Overall, I think I prefer using four pieces with (3)@1/2" + (1)@3/8".
Jerry