Thank you for both these posts, they are really useful. I've added the images credited to you onto the GTS website.
As to the pin trays / open salts, I'd say yes they could be dual function.
The 346 certainly appears to match the pintray shown in the 550 set photos.
I don't think 347 goes with 510, as the 510 is often seen with a small round pintray which might be 031, 032 or 033 from page 2 of the catalogue, but as you say those three are a better match for 530 than for 510. I suppose it would depend on what the buyers wanted as to what pieces were combined to make sets.
As to the big trays, the sets in the catalogue came with small (comb) trays, but as British consumers clearly liked the big trays in their sets, perhaps the buyers added larger matching trays to some sets to satisfy their consumers.
As the late Bernard Cavalot was fond of reminding us on the board, what the buyers for big stores wanted, they got. Just because the catalogue showed a set as A, B, C didn't mean that the manufacturer wouldn't mix and match so if the buyer wanted A, C and X, then they could have it, all in the interest of making those sales.

I think it would be useful to add the large trays as separate items in the Buder catalogue, as well as showing them with the sets they've been found with. I'll add that to my to do list. Thanks for all your very helpful suggestions.