Hope that this helped!
I think these are mainly based on the modern structure and, although they are certainly popular in the community, I have not been able to find any evidence for it. Although it is true that the cavalry ranks did look like that even further back in the day they did not by the napoleonic wars in the majority of units. Only the Household cavalry keeps that ranking structure until today (famously because of the fact that serjeant meant "servant").
After my recent cavalry hype wave I have yet again started to read through some of the manuals, namely...
"Instructions and regulations for the formations and movements of the cavalry" and
"The light-horse drill, designed for the use of the Volunteer corps of Great Britain" (just for the record this one is really easy to read and has pretty pictures
Both of these mention the words "Quarter Master", "Serjeant", "Corporal". (Still no sign of LCpl or Chsm, still only 'intelligent men', so I am also technically wrong in listing any of these, but I hope I explained myself sufficiently.)Rifles:
Your rifle ranks match up with what I have, so no disagreement there, in fact I'll add them soon. I think that Regimental Serjeant Major was an appointment, though. I will add a list of appointments later.Artillery:
I think that the term "battery" only later came into British usage, which is why I doubt the existence of a Battery Serejant or Battery Serejant Major. They also sound like appointments (I'll of course change my mind if I find sufficient information to indicate the opposite). Lance-Bombardier was a 20th century invention. They wanted to replace the rank of Corporal and therefore moved Bombardier up from the Lance Corporal equivalent to Corporal. As far as I am aware "Cannoneer" is/was only a rank in the US forces (perhaps also the Battery titles aswell?).
Saga's source also indicates that the listed ranks were in use, and as they are drawn from different records of establishments from the period they should be correct.
I feel like many American ranks and the Household Cavalry ranks circle around the community. This is of course no big deal, ranks are just names for levels in a hierarchy at the end of the day, but I hope to shed some light on the historical side of things. (But don't ask me about other nations, I know F**k all about the French, for example...)
Thank you for your reply, though, and especially the Rifle ranks! I'll add them when I feel I have added sufficient descriptions.
Also, I don't want to come of as just disregarding other people's suggestions (that would hardly be a discussion, would it?). I hope I have explained myself to a satisfactory level regarding the cavalry ranks and the artillery.
If anyone would like to have a look at the cavalry manuals listed I have a link to both of them as e-books, so just drop a reply here in that case. They should be easy to find through a search aswell. (They liked long niche titles!)