You've stumbled upon an interesting phenomenon, at least from researcher's (which I am) perspective. I haven't experienced this to a noticeable level, nor have heard it reported. However, it is well documented in clinical journals that a substantial amount of T3 (not sure of the percentage) and approximately 20% of T4 which I know for fact because of my studies in T4 to T3 conversion, occurs within the intestines (both large and small). I've cited a few such studies below if you'd care peruse them.
As such, it would make perfect sense that under the right conditions, such a portion of absorption could augment/ease defecation. And I'm glad you found something to relieve your straining, thereby alleviating your hemorrhoidal condition.
As for continued, i.e., long term use of Triiodothyronine (T3) or Thyroxine (T4), you are correct in that they can be safely taken at low doses for years without interruption. However, it should be noted that such use is prescribed for patients diagnosed with hyper- or hypothyroidism. This DOES NOT include the recreational use which we employ during cycle, as such continued non-prescribed use for off book (incidental benefits) would best be discussed with your physician. I have a feeling he/she will urge you to examine alternative digestive aids such as fiber supplements, enzymatic compounds, probiotics, etc.
Thanks for sharing this thought provoking discovery. Below are a few of the aforementioned references:
https://pubmed.ncbi.nlm.nih.gov/3049061/
https://pubmed.ncbi.nlm.nih.gov/33072620/
https://pubmed.ncbi.nlm.nih.gov/1612005/
Best to you.