When I read the etymology of the word faggot, I get a hint of its evolution from a noun pointing to an innocuous bundle of twigs needed to start a fire to a noun of intense derision. The word took on a distinctly negative connotation when a faggot was used to start a fire to incinerate a heretic. Since women have long been made subservient to men, applying the label would emphasize their undesirability & inferiority. Next, the word shifts to gay men who have been ostracized, fired, jailed, even executed for their sexual orientation.
I do not have the resources to take this theory to the next step, which would require examining more sources to see if the shifting in the target of the term is supported by evidence. When was the first time it was applied to a heretic or the event? What are the earliest examples of the word being applied to women; and then to gay men?
That is where I started. I had also checked the OED & found a similar record. Without the detailed information, it is impossible to solidly support this theory.
So do I understand that your goal is to disprove the findings of all other dictionaries, without already having evidence of your own as to why they must be incorrect?
Our dictionary gives the dates you need. OED will have snippet quotations and dates. Solidly support your own theory.
The fagot, musical instrument is called that way because it is made up of a set of six wooden cylinders, but they are aligned, it is a detachable instrument.