An alternative to microcontroller as a clock generator
Since your pattern repeats you can use a counter and a ROM. A clock to a binary counter chip and the counter outputs are the address lines of the ROM. The ROM contents are a truth table to create the output you need and the outputs are the data lines of the ROM. The clock can run continuously and as it wraps around or rolls over, the pattern will repeat (or several cycles will repeat - you can do whatever you want this way). It looks like you can use a very small 8 bit ROM, like a simple fusible link ROM. Could be a two chip solution or in a small FPGA. The CPLD might be OK as well. It looks like you don't need any flip-flops and it can all be combinatorial logic (unless you use a CPLD or FPGA and have to make your own counter).