A lot of good recomendations here, +1 on rem. 870's, mossberg 500"s are also good. Rem 870 is available in left hand model, but at a price penalty.

Also mentioned was the M37 Ithaca, which is quite good, and was quite popular with "leftys", another bottom ejector to consider would be the Browning BPS.

Left hand models have always been limited, but I have hunted and shot with a good number of left handed men& wemon who used right hand guns with no trouble, Bolt action rifles included.

A .22 auto is also very usefull, and near the top of my "must have list". The Ruger 10-22 is one of the best, but you stated that take down capibility was important to you.
The only take down .22 auto that I would put in the same quality/ accuracy/dependability with the 10-22 would be the discontinued Browning. Another popular option would be the lever action Marlin 39-A

I know there are a lot of AR7, and Marlin Papoose fans , I just don't think these quite "stack up", but they are available and economical.

Good luck with your selection.