This is all correct, except that the Otto Link Four**** mouthpiece (produced from 1935 till 1940) was the model before the Tone Master came (from 1940-1945 the normal TM, from 1945 till 1949) the improved TM). Normally Tone Masters went up till about 5*, the later improved TM had some bigger facings (going to 7 or very rare higher) and a slightly smaller chamber and slightly more baffle than the first TM models. The earlier Four**** didn't have a baffle and a slightly bigger chamber than the first TM (and also a different ligature).
I've never seen a RR Crescent, but (as mentioned by Raghav) all the RR pieces I've seen are remakes of older models on steroids and by far not equal to the original Otto Link designs. Which means that the RR's will play more bright/modern and will have bigger tip size options compared to vintage Otto Link's. I currently own 4 Four**** pieces and 2 TM's (but I've tried more of them) and from those only my refaced TM (from 5 to 8, I bought it like that) plays really well for me (but I'm a big tip player, the smaller tip pieces don't work for what I want from a mouthpiece).
If you're curious to play a bigger TM tip piece you could also try to find a New Vintage Tone Master (they are still produced by Otto Link and are more close to the old 1940's TM than the RR ones). I have a modern NV TM 10* and compared it many moons ago to my refaced old TM 8.
See these clips when you're interested how they compare in sound when played by me (in a ballad and a free style recording):
1a. 'Someone To Watch Over Me' (refaced vintage improved Tone Master 8 - La Voz medium):
https://soundclick.com/share.cfm?id=12325863
1b. 'Someone To Watch Over Me' (modern New Vintage Tone Master 10* - La Voz medium):
https://soundclick.com/share.cfm?id=12325879
2a. 'Waterwings' (refaced vintage improved Tone Master 8 - La Voz medium):
https://soundclick.com/share.cfm?id=12332757
2b. 'Waterwings' (modern New Vintage Tone Master 10* - La Voz medium):
https://soundclick.com/share.cfm?id=12325305
And one more clip done on the fully original 1940's Tone Master 5*:
3. 'Honky Tonk' (original Tone Master 5* - La Voz medium hard):
https://soundclick.com/share.cfm?id=13063225