Simplify with Assumptions Sqrt[(expr)^2]

It would appear that you can increase the number of assumptions variables that Mathematica will handle by altering a system option:

SetSystemOptions["SimplificationOptions" -> {"AssumptionsMaxNonlinearVariables" -> 5}]

Simplify[Sqrt[(x - y + a b c)^2], x - y + a b c > 0]
(* a b c + x - y *)

Simplify[Sqrt[(x - y + a^2 b^2 c^2)^2], {x > y, {a, b, c} ∈ Reals}]
(* a^2 b^2 c^2 + x - y *)