[Edit. Forgot to escape the angle brackets, darn it!]
With の I was reading it as “wanting-to-lend-a-cat-a-hand-level now-boredom”. That is, an entire noun phrase where everything modifies the final noun, 暇.
With a sentence fragment like this, I was interpreting it as effectively saying “<adjectival modifiers> boredom [exists]”.
But I think the core sentence is actually a copula. It’s coupling “now” and “<adjectival modifiers> boredom”.
Very hard to express without the diagrams!
With diagrams: The の version in my head, the subject was “boredom” and looked like this:
While the actual は version had a subject of [@] (standing in for “now”) and uses a copula:
Since it’s just a fragment, the 今の暇 version could also have been a copula like:
◯ [が] 暇 [だ]
Since it’s just a fragment, we have to supply something to turn it into a sentence. My brain wanted to add “exists” (an “action”, an “A does B” sentence), though, rather than the copula version above (an “A is B” sentence). I think a Japanese native would tend to assume the だ version even without the explicit topic (though I’ve no proof of this).
With は, it has to be a copula, and making 今 the explicit topic emphasizes now over boredom (imo).
EDIT:
Interestingly, I don’t think there’s any way to capture this difference in natural-sounding English. You have to use the stilted “transliteration” forms in the diagrams.
In English, we’d say “I’m so bored right now I could lend a cat a hand”. We would automatically add an explicit subject and create a complete sentence.
After further thought, I guess we’d change the emphasis purely with word order, “I’m so bored right now …” vs. “Right now I’m so bored”. This has a similar nuanced difference to me between the の and は Japanese versions.