We have a high rise with several hundred analog connections, mostly due to fax machines and use ASU-II's which do really well and aren't prohibitively expensive.
I find these are OK up to two of them... or 96 ports... Once you starting getting into triple digit analog POTS extensions, using ATAs makes a lot more sense cost wise. OP had 340 analog extensions, which would require 7 ASUII with two 24-port cards each, and one with a single card for 8 total. I am not against ASU's at all, but at this scale I would look at a different solution.
That said, on the secondary market these are getting pretty cheap, if you have enough CIM ports on your chassis.