The camp fire would explain why the shape of the butt stock is unusual. You can see burn marks at just that point. As for the front-end, if you family history says it was not altered, then perhaps there was an owner before your great grand-dad who chopped it down, OR maybe the camp fire damaged it and it had to be lopped off. BSA never shipped a commercial fore-end with that length and shape.

You wrote:

The bottom one in that photo has a 24 1/2 inch barrel, so it cannot be that one, unless the barrel was cut down at some point. The barrel was not replaced, because the numbers match the rest, and no old numbers were struck out. The top two rifles on that catalogue page have 19 inch barrels, so they are candidates, although they have wood checkering that I cannot see in your photos. The No.3 pattern lacks checkering but has a 21 inch barrel. Yours could be a No.3 Pattern that was ordered with a custom length barrel, which was possible. I suppose everyone has figured out by now that it was not a service pattern Long Lee that was cut down, because there's no provision for volley sight. But the others features make it clear that it wasn't a factory sporter. The Military Pattern (i.e., Trade pattern) Officer's Carbine is the best candidate.

Eager to see the entire side view, from Left and Right.
..

You originally asked about its value... The magazine and the original backsight (if you find it) are together probably worth nearly as much as the rest of the rifle. Save that brass oiler and the cartridge (that is amazing)...when they are cleaned up, they might provide more clues.