I think u r right to be worried about the g3 lines against the CC def.
1.d4c5 2.d5f5 3.c4g6 4.Nc3Nf6 5.Nf3d6 6.g3Bg7 7.Bg20-0 8.0-0Nbd7 9.Qc2Rb8 10.a4a6 11.h3b6   difficult to see how B gonna develope in a v cramped position.B cannot get rid of the backward e pawn without incurring deeper weakness.W has a small but nagging advantage.Esentially the potential for B ot err is greater than W.B i feel is only fighting for  draw.
My suggestion use CC depending on the opponent.Dont adopt it as a mainline defense against d4. Good luck .

Does Black get enough play in the Clarendon Court defense?

I've heard there's a "Foxy Openings #1" video on the Clarendon Court by GM Jonathan Levitt.

I'm not particularly worried about White's tries for direct refutation (3.e4, 3.h4, 3.Nc3 Nf6 4.f3, etc.). White will probably have difficulty even reacting to d4 c5 d5 f5.

My biggest concern is the positional g3 lines (with or without c4), where Black fianchettos the f8 Bishop. But my concern is that Black doesn't get any play since there's no pawn break for Black.

I'm rated 1980 USCF and I'm currently playing 1.d4 e6 2.c4 c5 3.d5 exd5 4.cxd5 d6 as Black with relatively poor results (the problem being a lack of space and piece play), even though it looks like Black has a nice position.