9:11 - Actually, I must correct you there: The SL-HF450 has two heads and provides reasonably clear special effects on βIII only. The SL-HF550 has three heads and provides true, clear special effects on both βII and βIII. (On some SL-HF450 machines, the frame advance and slow motion controls are labeled to say they are designed for use with βIII.) I think the '450 and '550 were introduced at the same time, in 1986. The '650 was introduced later, in 1987. I found a Sony sales brochure from early 1986 listing the models being sold at the time: SL-100, SL-HFR70, SL-HF450, SL-HF550, and SL-HF750. It listed a series of possible features, like "BetaScan", "BetaSkipScan", "Freeze Frame/Pause", "Crystal Clear", "Frame-By-Frame", etc., and marked each with "Yes" if the machine had it. Only the SL-HFR70, SL-HF550, and SL-HF750 had "Yes" for "Crystal Clear". (Curiously, the SL-HF450 has a synchro-edit feature, but the SL-HF550 does not!) 28:31 - Don't forget about the 3D-printed gears someone made and is selling on eBay. TH-cam will not let me post a direct eBay link, but you can find them by going there and searching for "sony betamax 3-684-163-01" and "sony betamax x-3684-123-1". I don't know if those are the gears you need, but you should look at them anyway.
9:11 - Actually, I must correct you there: The SL-HF450 has two heads and provides reasonably clear special effects on βIII only. The SL-HF550 has three heads and provides true, clear special effects on both βII and βIII. (On some SL-HF450 machines, the frame advance and slow motion controls are labeled to say they are designed for use with βIII.) I think the '450 and '550 were introduced at the same time, in 1986. The '650 was introduced later, in 1987.
I found a Sony sales brochure from early 1986 listing the models being sold at the time: SL-100, SL-HFR70, SL-HF450, SL-HF550, and SL-HF750. It listed a series of possible features, like "BetaScan", "BetaSkipScan", "Freeze Frame/Pause", "Crystal Clear", "Frame-By-Frame", etc., and marked each with "Yes" if the machine had it. Only the SL-HFR70, SL-HF550, and SL-HF750 had "Yes" for "Crystal Clear". (Curiously, the SL-HF450 has a synchro-edit feature, but the SL-HF550 does not!)
28:31 - Don't forget about the 3D-printed gears someone made and is selling on eBay. TH-cam will not let me post a direct eBay link, but you can find them by going there and searching for "sony betamax 3-684-163-01" and "sony betamax x-3684-123-1". I don't know if those are the gears you need, but you should look at them anyway.