i.MX6S has 624 balls and it's available only in that package, unless you need exactly that processor or need all it's features then go for something in a smaller package.
i would suggest to go for the Sitara cpus from TI as others suggested above. If you don't need the industrial stuff like profinet,EtherCAT, EtherNet/IP (it has nothing to do with the regular 10/100/1000 ethernet which is present in all siatara 335x chips) then you can go for the lower ones - eg. you can have an AM3352 without 3D accelerator (ideal for headless systems) and without industrial interfaces under 15Eur (14.50eur in single piece @farnell) AM3354 with 3D and without industrial ifaces is approx 19Eur. and those Sitaras are coming in a friendly 324ball 0.8mm pitch backage.
btw.. i'm on a similar boat . need a small , relatively cheap and readily available linux system, raspberry Pi zero is unobtanium in quantities bigger than one single piece. and all other single board machines are either too big or too expensive and all of them have too much HW i don't need. so currently i'm working on a design using the AM3352.