Earlier quoted context omitted.
If feasibility is your goal then cp/sat solvers/heuristics should be your tool of choice. I you have optimality requirements (aka from the feasible solutions find the absolutely best) then optimization is the way to go
I think that you've misunderstood what I said. For large instances of this specific problem (and when the time limit is too short to allow either CP-SAT or CPLEX to prove optimality) the best integer feasible solution found by CP-SAT is generally of better quality (w.r.t. the objective value) than the best integer feasible solution found by CPLEX. Furthermore, in some cases, CP-SAT can offer a certificate of optimali…
My advice is if you are on the clock, just use whatever works best out of the box.
Now if you plan to solve this problem thousands of times daily, then I would invest in writing custom callbacks in CPLEX to inject feasible solutions during the search since its heuristics are suffering in your problem case.