How to use HDL designs in hobby circuits and how to do transistor level tuning
What you are asking to do is nothing any hobbyist is able or afford to do. You can create your design in HDL, test it on FPGA, and prototype it on a demo board, but the going from FPGA design into ASIC is a whole different ball game.

Making an ASIC is a very complicated and costly process. And requires both VERY expensive tools and knowledge on how to use them. 

If you design is not very complicated and large and you are not expecting to sell it in 10k+, you should definitely look into low cost FPGAs as an alternative to ASIC. You can get FPGAs for as low as $1 is larger quantities. 

And since you are talking about hand soldering the products, I don't think ASIC is the way to go for you.

Just my 2c!