One of the advantages for the Vasari, and to some extent the Advent are that they can mine any system.
I see two problems with this:
1. The mines are free and TEC's are not.
Now this isn't necessarily bad, but in it's current form it is a severe problem with balance
2. TEC can't mine neutrals
I propose that the TEC starbase can also lay minefields - I know it's problematic in its current form, but I have hope!
First add a special constructor ship for mines and mines only. It sucks that currently if you are building anything else the mines get build last.
I like how TEC gets to place their mines, and I think adding in a mine-only constructor ship to the SB would work.
As for how to handle it, make it part of the level 1 factory upgrade. If you can build ships when why not be able to build a little guy to help lay mines. You can even increase the cost of the mines if needed.