No, unfortunately Factorio only allows one rocket to be assigned per silo type; which is also why Spaghetorio uses 4 different silos. I'm afraid you'll have to pick your favourite.
Out of curiosity, how hard would it be to create a mod that just adds Spaghetorio's 4 silos and rockets so they are available in addition to the vanilla? Identical stats to existing for quality etc, just alternate visuals.
Not hard at all but certainly out of the scope for this mod. You might find someone interested in doing this in the factorio discord; if you decide to make it yourself let me know when you've released the mod and I'll link to your mod from this mod page!
Something I am considering, since that would be much easier than my other plan, which is to make a vehicle from an exported Space Engineers ship model. Just going to be one of those time/energy things for me. Thank you for the responses as well. I will probably give this one a go for now to have something different (especially since I don't see any other stand-alone rocket sprite alternatives for Space Age).
