Yes, the 3800/3880 are great printers.
I have never tried, so can't say if the 3880 could print on roll media- but suspect even if you made a roll holder, that the printer may get confused when it still sees paper after the print, and may "eject" excessive paper and un-roll your roll of paper. It's certainly worth trying, but I suspect the paper sensor will go crazy.
I think the 4880 is a great model (yes, the 4900 is problematic, as well as the 7900/9900 and 7890/9890- though some are working well, others are nothing but problems). My personal all time favorite model is the 7880/9880, but they were discontinued and can be difficult to find a decent one. If you get a 4900, 7900 or 7890- make sure to get the extended warranty, so you're covered when issues arise.
Sorry I can't give a good answer to this question, I'm in between the older great models that were unfairly discontinued, and the current models that are headaches.... maybe there's a good solution in the future (but it unfortunately looks like Epson is moving into the commercial printing market, and away from fine art)?
Please do let me know if you try printing on roll media with your 3880, I'm curious...
All the best~ Dana