I would look at still using a compact logix PLC since it is what you know. Pick the lower level processor - an L18 or so and use a remote I/O system with it - such as Murr elektronik Cube 20 system.
The Murr I/O is 1/2 the cost (or less) of the Allen Bradley I/O cards and works just as well (Better, IMO, since it is more flexible).
I'm guessing you could get the PLC for around $1.5k
(Take my below estimates with a grain of salt, it has been a few years since I've priced this stuff)
You need 6 16-input cards - but the Murr comes in 32, so 3 of those at around $200 a piece is about $600. 2 Digital output modules at $300 a piece is around another $600, plus the bus-node for another $300 or so.
Controller: 1.5k
Busnode: $300
Input cards $600
Output Cards $600
Outside power supply $300 (assuming ~ 20A 480/24VDC power supply)
About $3.3k give or take. Plus, you don't really have to learn any new software.
If you don't like the Murr, you can look into other IP20 remote I/O options: like the Weidmuller stuff (which I really like for inside panels). What makes Murr special is it all works on a single IP address, so you don't need an expensive controller to do a ton of I/O.