The cost you are talking about are for massive production right ?
I think OP was talking about building just a prototype for personal use.

It wouldn't have to be miniaturized (one can easily find some square meters to put a miner if it is profitable).

I know nothing about ASICs, I just read the wikipedia page, and I am not good in electronic either, but mining algorithm aren't secrets.
Would it be so hard to build a mining chip with basic electronic components ? (I guess the answer is yes, else someone would already have done it)