OP could only use ASIC if his work included only doing SHA-256 hashing over and over.
I'm not sure you realize that ASIC stands for Application Specific Integrated Circuit - it's a cover term for any sort of circuitry (silicon based or otherwise) that performs a specific task or set of tasks. GPUs and CPUs are both arguably ASICs - just performing a very generalized set of tasks.
There's more to ASICs than just bitcoin. Bitcoin is a niche within a niche, in terms of global semiconductor manufacturing.
Unfortunately most bitcoin miners are trying to minimise their capital by making open air designs that arguably are not suitable for OP. That way they reach ROI much faster. Wheras in OP's case it seems that they have more or less limitless money to throw at the problem. Good luck with that.
The OP is trying to do something resembling a professional OpenCL cluster for production work, which is very different from bitcoin mining. I'm somewhat surprised how many people in this thread didn't even read his requests about having something in a case that was rack mountable. Most data centers will laugh you away if you show up with milk crates for their racks.
This is actually where fpgas can come in handy, if he's doing the same type of processing over and over, otherwise gpus would still be preferred.
FPGAs are certainly reprogrammable for different tasks. The main problem is that writing the hardware description (in Verilog/VHDL) is much harder than the parallel coding for GPUs, and depending on the task, the insane memory bandwidth of GPUs may be of significant use. For large data processing, the onboard memory and bandwidth of GPUs is incredibly useful, and generating FPGA boards with the same capacity would be significantly more expensive.