If I understand the problem correctly, this is the solution:
solution
a = 2299200278
b = 2929959606
c = 2585800174
d = 3584110397
I solved it with Z3. Took less than a second of computer time, and about an hour of my time -- mostly spent trying to remember how the heck to use Z3 and then a little time debugging my initial program.
Frames Per Stratum