I attempted to search for a complete diet I could make myself and I didn't have any luck with any simple or affordable options.
Cheap cat food is full of ash and other unwanted filler. Game bird feed is less than $15 USD for 25kg (just checked the size of my bag). I can't imagine cat food similar to that price being good for even cats. Cheap cat food is linked to many cat health problems that could be avoided with a higher quality feed with less filler.
I still suggest you make the effort to get the proper balanced food because even if you use a homemade recipe, you're likely going to have to go to the feed store anyways to get the mass amounts of grain and etc. ingredients. You need a specific percentage of protein, fat, fiber, calcium, selenium, phosphorus, sodium and other vitamins or their health will suffer.
There's also the problem with making it into pellets as even if you have a proper mixture of several ingredients, the quail are likely to pick and choose what they want to eat instead of getting balanced nutrition like a pellet offers.