If you go with one of those ^^ or any other KM vase, you will need a size 30 gasket. Personally I think a size 30 vase is too big for the AF medium as the proportions will look bad IMO and I don't like the water level being up in the neck area.
Those Mya bases you linked to most likely will not fit. The large Mya bases have ~1.5" openings if I'm not mistaken but the shank of the AF medium is also 1.5". If you get lucky and get a base that is slightly over 1.5" then you might be able to get it to work using only tape as a gasket. I wouldn't recommend risking it because if it's 1.5" exactly or smaller, it won't fit at all. The screw on types will definitely not work.
You're best bet is to find a size 26 vase that's 9-10" tall. I use a Syrian vase now because I didn't like how small the footprint is on the one it came with. Here's a pic of mine: