Council of sages, please opine:

Your intrepid hero has both Unexpected Courage attached, as well as Caught in a Web. May he/she still ready via exhaustion of Unexpected Courage -- without needing to cough up a pair of resources -- provided said exhaustion and readying takes place in any phase other than the refresh phase?

For the benefit of those without ready access (or desire to presently consult these cards ), the text of Caught in a Web reads: "Attached hero does not ready during the refresh phase unless you pay 2 resources from that hero's pool." (Emphasis added). So the limitation would appear to apply exclusively to the seventh and final phase of the round, the "refresh phase." In other words, seems that the simple wording of the Unexpected Courage Action, "Exhaust Unexpected Courage to ready attached hero," when used in phases 1-6 of a round, would not conflict with the Caught in a Web prohibition.

Appreciate your learned judgments!

You can exhaust UC at any time to ready the attached hero. The web affects the hero's standard refresh readying, and does not counter the readying effects of other cards like UC.

Thanks ArachneJericho -- it just seemed to good to be true at the time, in at least partially thwarting the effects of Caught in a Web, that I really wanted to see if I was totally out on a limb or reading the card interplay correctly.