Welcome, Griffis
Tenor banjo for ITM is commonly tuned GDAE. That tuning is good for tunes in G and D (which covers most ITM), and for fiddle tunes in A. Quite a few sessions will include the odd American tune in A. The tuning was probably mostly popularised by Barney McKenna of The Dubliners, an absolutely brilliant banjo player. Personally, I also prefer the GDAE tuning over CGDA for ITM.
I think Gerry O'Connor plays quite a bit in CGDA, but all the tenor banjo players I know personally use GDAE.
The problem with chords is largely down to the physical characteristics of the instrument. That tuning is at the limit of how low a tenor banjo can really be usefully played - especially the short-scale version. The low G can get really slack and hard to tune and intonate accurately. What's more, the scale length is short, but the bridge doesn't allow compensation in the same way that a mandolin bridge does.
To be blunt, chords on a GDAE tenor are usually going to sound a bit carp. It is really a melody instrument.
You'll find that chord/harmony playing in ITM is a recent development and one not universally embraced. The tradition - especially the dance tunes (jigs, reels etc) - is mostly one of melody instruments playing in unison.
As for using 4ths or "Chicago" tuning, I agree that is admitting defeat. Part of the experience and character of various instruments is learning the tunings and their strengths.
I have a friend (primarily a guitarist) who also plays both tenor banjo and mandolin in guitar DGBE tuning. I don't really consider him a banjo or mandolin player.
Good luck with the banjo.