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(No, this is not an agenda thread.)
It is possible that what you observed as spurs and harmonics and the receiver “protection circuit trip” was caused by it being overloaded by being too close to the transmitter. Though the field strength produced by Part15 FM transmitters is puny, it is very strong near the transmitter.
Maybe before expending all the effort on the transmitter you can try moving the receiver away from the transmitter and/or checking the signal with another receiver also not too close to the transmitter.
Years ago I built a one transistor FM transmitter and had a lot of trouble tuning it. I would set the receiver on an empty frequency and would hear several signals as I rotated the tx. tuning cap. I also heard many “images” up and down the FM band until I moved the transmitter across the room and then only heard one signal. This is what makes me think it could be that your signal is too strong for the receiver and maybe it is not dirty.