Unusual vs. Unusual with clubs

[Antrax]

Playing Unusual vs. Unusual, i.e. when the opponents show a two-suited hand, cue-bidding the lower suit shows something in the lower remaining suit and cue-bidding the higher shows the higher:

Partner opens 1♣ (3+), RHO bids 2NT (in this case, reds). You hold a limit raise in clubs, so the system bid is 3♦. It's not very efficient as partner has a minimum and no stoppers to show, so we end up in 4♣ which is too high.

I'm guessing there's some standard interchange here? How do you handle defense vs. two-suited overcalls when their lower known suit is higher than your known suit?

[the hog]

With a limit raise in C bid 3C. 3D shows a forcing hand in S, 3H shows a forcing C raise, 3S shows a limited hand with 6S, nf

[aguahombre]

With a limit raise in C bid 3C. 3D shows a forcing hand in S, 3H shows a forcing C raise, 3S shows a limited hand with 6S, nf

Yes. "lower for Lower" should mean lower for "cheaper".