Cat urine on wool rug - get it really wet?

I have cat urine in the rug - didn't catch it in time to sop any up.
I have it outside, and have been using vinegar and "urine off".
I have done this successfully in the past, but not remembering exactly how.
I'm wondering if I should get it soaking wet (the section that stinks) and leave in the sun, or dry with towels to absorb some.
Same with the vinegar and "urine off". Wet it first and let it soak in? Just let the sun dry it, or get some off with a towel?
Every time I get it wet (I've been letting it get wet and dry in the sun) i am amazed how much it still stinks!

My current plan is to put it on the deck and get it totally soaking wet, put it upside down (on some chairs to get air on all sides) so water will drip out of it (hopefully with some urine smell). Then go back to the vinegar solution.

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