I wouldn't have used a paddle to stir it up. If I thought it were stuck, I would have re-sealed and gentle agitated the sealed fermenter gently to re-suspend the yeast.
If you did that today, I wouldn't bottle, I'd wait a few days, (a) to see if you drop a few more points. And, (b) To let all the trub you kicked up fall back down and let the beer clear a bit more, since all that beautiful 4 weeks of patient clearing has now gone away for a bit...So just let it re-settle for a few days.
I find that anything below 1.019 is okay to bottle...I've even bottle a 1.020 that had stayed that way for several days...anything above that I feel is a risk for bottle bombs.
Also a 2-4 points above the expected FG range is no big deal....
Since you agitated and warmed, you'll probably get a few more points over the next few days, as the yeast wake up from their snooze.
(If you have a sanitized jar, you can save the sugar water in the fridge...just reboil and cool on the NEW bottling day. Or since you have some "simple syrup" now, whip up a batch of Mint Juileps with it.)
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