13mm is just a hair over 1/2" (0.512 vs 0.500) so 5/8" is the next size up (0.625) so you'd have to add tape to the 13mm motor to build it up to 5/8" thickness. https://www.mcmaster.com/2197k11 that'll get ya 5/8" ID with 1/16" wall thickness. Less than $9 for 3 ft.
I doubt it would lift the entire 3ft but it *might* lift 6in of it. I think CF might be a better option at this size due to the weight. Closest I can find in CF is 3/4" ID at $25/ft that would work for 18mm. Or you know.....cardboard tubes.
If you need more strength/stiffness but increasing the diameter and mass a bit would be OK, you could consider wrapping 3/4 oz glass cloth around a paper 13mm tube, using a good quality epoxy resin. Just I can't tell from your posts what the specific need is for a fiberglass tube.
Worst-case, 13mm drill rod could be used as a mandrel for making an all fiberglass tube. After a good coating with spray on mold release before layup, the ID of the resulting tube should work for holding a 13mm engine.
Having personally made all-glass competition tubes, I can vouch that it's a certain amount of work. Usually you do it to *reduce* mass - 3 wraps of 0.7 oz cloth will end up at around 1/2 the mass of a paper tube but it's pretty fragile and bendy. You can use more wraps or heavier cloth to get a sturdier tube, or just glass over a paper tube like George said. You'll get a stronger tube doing that if you peel off the glassine layer first (if there is one).