While it’s still at the CAD stage, perhaps you might think again about the trumpet. It’s likely that in the 1770s they were still using the single-loop long model trumpet , as shown in the Troiani picture. The short model, double loop type doesn’t appear in any pictures that I’ve seen until after 1800. Simkin's work, though very nice, is often somewhat mistaken, and I'm not sure where the more recent painter got his info.
If there's someone who knows of a contemporary 1770s picture showing the double-loop short model I should be very interested to see it, and will willingly eat humble pie.
The famous Stubbs painting of the 10th LD of 1793 shows the long model . I have such an instrument, and to help with scale , it’s 28” from the lip of the bell to the back bow. The mouthpiece pipe normally stuck out beyond that for a couple of inches .
The front bow of the tubing normally went right up to the lip of the bell at this date, to which it was wired for strength .
The Light Dragoons also had hornists, playing French-style hunting horns, and being Dragoons they also had drummers , but I think those were dropped fairly early on.
A hornist can be seen on p.47 of Barthorp’s” British Cavalry Uniforms” .