Update after consulting with raiguard on discord:
I've discovered a 'hidden' flag for items that would allow me to hide the extra spidertron variations from things like filters and Quick Item Search. I am hesitant to actually apply it though, because I was under the impression that you might want to be able to do that because you might have 'Flamethrower Spidertron' in your inventory/storage if you pick up a spidertron whilst in flamethrower mode. However, I've just tested this, and it seems that whatever mode it is in, it will always revert back to 'rocket launcher spidertron'. I don't know why it does this, perhaps you'd be able to confirm that it happens to you as well? If it is truly the case, then that is excellent!
I will use the 'hidden' flag on the shotgun, and on the waypoint and patrol remotes from Spidertron Waypoints (unless I implement your suggestion there to make each mode persistent per remote :) ).
The reason the shotgun appears and the others don't is because the others are all based off of vehicle weapons, so they have already got the 'hidden' flag.
I'm still not sure why the spidertron variations don't take the colour of the MK2&3 spidertrons, but this occurs in the base game as well (in filters and logistic requests), so it is definitely a bug on my side, to do with how I integrated with Spidertron Extended. I don't see this as a major issue though :)