You stated in one of the posts that you have hard water. This can lead to a tiny amount of solid interfering with the fill valve.
I used to have a painfully slow-to-fill toilet. There was no problem, as you have, with any clogged waste lines. All I had to do was take the top off the fill valve, I believe the Fluid Master website has instructions, and flush it out. It takes more time to explain it than to do it. Whatever debris I had in the valve was removed and the fill valve operated properly. Another good website is
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In your case, it appears that there is enough debris to keep the fill valve from completely closing so your toilet keep running. Replacing the valve, etc. will help in the short run but eventually, I anticipate that the problem will reoccur as more debris builds up. Perhaps you can have a filter or water treatment process installed such that mineral deposits do not build up in your plumbing.
Good Luck.