Is it possible to use different combinations of weapons for the spidertrons? I'm looking at my crafting list and have a few different weapons systems I'd like to combine but it doesn't seem possible?

It is possible, and I have really tried that.
(My initial plan was to provide like only 4 variants each having its own suitable weapon set; instead of the current scheme of 13 variants each having the same weapon.)
The results, however, were highly unsatisfactory.

The main problem appears when weapons have different ranges, the game will NOT switch to the right weapon for the Spidertrons.
For example, I have provided a set of: weapon A (range 30) on slot 1 + 2, and weapon B (range 20) on slot 3 + 4.
Now you build one and use it to attack spawners. And a small worm (range 25) is targeting your Spidertron.
You hopefully using the long range of weapon A to snipe the small worm, so you move your Spidertron at a distance, say range 28.
Now your Spidertron will only fire one shot from slots 1 and 2. It cycles to slot 3, but will stuck there forever, because weapon B at slot 3 do not have any valid targets.

Solution 1 to this problem is removing ammo from slots 3 and 4 (as weapon cycling will skip empty slots), but this may not be obvious. Especially for players commanding multiple Spidertrons, how many of us really have time to look into each Spidertron whether they are stuck on firing or not?
It is very likely that some users will complain, where I have provided weapon combinations that are not working.

Solution 2 is much simpler: do not provide such choices. Then users will not complain my mod is faulty.

There is another problem for providing different combinations. The placeable grid list ("Placed in:" field) under equipment tooltips are already quite long (from my 13 weapon choices, and 3/4 tiers each...) The permutations of 13 weapons on 4 slots (even under weapon class restriction) would be a much larger number than current.
Until there is a way telling the game to hide "smartly" the similar Spidertron entries, I do not want to worsen the situation.

Well, getting to see the reasoning behind it not being in the mod as is makes quite a bit of sense, so I do thank you for sharing the reasoning. I do agree on the not wanting to check multiple spidertrons, as I have a squad of 9 that I use, and that would be painfully annoying to go through

I do hope that it becomes possible later down the road, but I won't hold my breath on it as it's likely not something that's a high priority for Wube to implement into the game code.

I also wonder why the firing mechanism is not "smart" enough to cycle only weapons with valid targets, when I was creating this mod.

However, I could also guess why. Spidertron was a surprise feature for 1.0.0, but that also means it was a rushed and untested product. It was designed to wield the quad-rocket launcher only, so not surprised that they did not expect different weapons of different ranges.

I have the same expectation as yours. I do hope that such support will be provided in future versions.
In reality, however, there are already a long (and expanding) list of modding interface requests (including several of mine) on the forum still left untouched for months (if not years).
Not to say the worst part: GUI support. Some dev (e.g., Klonan) has explicitly mentioned they are not willing to provide more GUI support unless it is used by vanilla. There is no hope to get even some "elementary features" (considered by modders).
Therefore, I should say I am quite pessimistic when the devs will act on that.