Gate array??, I think you would be better off with a (C)PLD.

For an introduction to what a PLD is, have a look at first 16L8 then 22V10.

After that have a look at the larger offerings from Lattice Xilinx etc. some of these are ISP and, most often the software to program them is free.

For a simple application like the one you describe the language of choice for programming the PLD would be CUPL or abel. The more advance Verilog and VHDL take a long time to grasp.
I do not know about all of them, but Lattices free software can work in "schematic capture" where you feed a schematic using 74xx gates to the compiler.

Erik