I notice that you continue to ignore the advice -- made for several of your earliest (of many) Questions in this long saga -- that:
1) inert `Sum` may be more suitable than active `sum` to your overall investigations and more particularly your attempts at symbolic verification
NO, I am not ignoring anything. I include both INERT & ACTIVE sums, for my sake, to indicate that indeed the 2 produce the same results, but the 2 commands do behave differently. KEEP IN MIND that you know the inner working details of MAPLE. I do NOT. Before all of this work I did not know about INERT vs ACTIVE. I picked up MAPLE as a tool for research purposes & have learned it only through trial & error & interacting within MAPLEPrimes. I have had no formal classes or training with using MAPLE code.
2) `add` (under evalhf, or Compiled) would get far better performance than `sum` and likely exhibit less roundoff in the case that `sum` or `simplify` or `combine` produced trig terms with large rationals.
This I will check out.
Regarding the issue in question I am working with what you provided to digest what is occurring & likely will have follow questions.