Monster cables have a dodgy reputation for not always being what they're cracked up to be, especially in analog video applications. Forget trying another fancy cable, try the cheap RCA cable that came in the box with your Magnavox or any other piece of gear you own. If that solves your problem, then there's something funky with the cable you were using. (There is no audio input option on any DVD recorder aside from RCA stereo analog.)
If the problem was in your cable, its almost certain the sound would be funky at every recording speed, not just HQ. If the sound is fine at SP with this motorcycle race dub, and the sound is fine at HQ when dubbing other shows, then its just one of those infuriating random glitches that sometimes occur with AV gear even at the pro level. Sometimes you just have to live with workarounds: use SP for that channel and stop stressing. (If I'm reading you wrong, and you're having this sound problem at HQ speed with ALL dubs from FiOS, there may be something wrong with the recorders external sound processor.)
A test you can try: see if you can receive at least one broadcast or FiOS channel using the coax tuner input, and check the HQ sound thru the tuner. If it records OK thru the tuner, then the FiOS box might be overloading its line outs. This can happen if your FiOS box has only one set of audio line outs and the box is controlling the output level from its remote: if you set the volume too high with the onscreen display it can overload some types of connected gear. Try lowering the volume on the FiOS box to a bit more than half, see if that helps any.