Bruce L. Bergman writes:

http://www.truetex.com/carbonation.htm

Right! But it's a heck of a lot easier to leave the valve stem in
the schrader valve on the cap (like the Camel fitting you have in the
first cap photo) and use a schrader chuck rather than your ball valve,
pressure gauge and Milton QD hose fitting. Plus, the modified bottle
cap automatically holds pressure until it is unscrewed for dispensing
the product, even with the hose disconnected.

It is difficult to hold a tire chuck on a valve stem while agitating the
bottle. It also wastes some gas leaking out the gasket. You need the
ball valve to stop the slow leak of a chuck when the system is not in
use; this can bleed your CO2 in a matter of days.

If you really want to do it like you suggest, then a better approach is
to buy the ball lock fittings and cap instead of improvising from a tire
valve.

I've long ago given up on making my own, when there's Item 30 -
Costco Simply Soda diet is like $2.79 a case, which is cheap enough
that it doesn't make it worth messing with. But if I ever run across
a good used BarMate gun, chiller plate and carbonator pump at a decent
price, I might put it all together and start making my own again.

Any on-tap system has an unavoidable constant-bleeding overhead from
having to run a chiller. Unlike the bottle method, you have
convenience, but not economy.

Oh, and use a regular air compressor to run the bag-in-box pumps,
it's a lot cheaper than wasting CO2 on it.

Not really. The volume of CO2 gas to pump the syrup for a given amount
of beverage is a tiny fraction of the CO2 gas needed to carbonate that
same beverage, so any savings in CO2 by using compressed air is
necessarily marginal. Plus you then have the added overhead of having a
compressor always on duty (slow leaks = money), and the problem of icky
shop air contaminating your beverage system. Having an air compressor
running (intermittently) all the time also worries me; they seem like
the sort of thing that could kick on and overheat or malfunction while
you weren't home.