You did say ANY suggestions:

Try on a NEF/H&R 1871 single shot heavy bbl, they're really cheap, but probably as well made as anything out there. The way they break, they're as easy to break lefty as they are righty...I shoot a Buffalo Classic .45-70 left handed quite a bit (even though I'm really right handed, it's good to be proficient both ways). Once you get used to shooting it, you'll likely find it as accurate as any factory heavy bbl bolt gun out there, I know mine are!!!

Typically .22-250's come in a little longer bbl than 20", I'd say no more than 26" however. I've got a 22" standard bbl, 24" heavy bbl, and 26" heavy bbl, the velocity change between the 24 and 26 isn't much, and the distance between the 22 and 24 isn't THAT much bigger, but there's quite a difference between the 22 and 26.