I have a 6'x2'x2' tank and sump that holds probably around 180 total
gallons of water. My tapwater is initially around 3 dKH and about 7.6 pH
(tested using Aquarium Pharmaceuticals tests). I added a couple
tablespoons of baking soda to raise the carbonate hardness to 6 dKH.

You did not need to change the KH.
Add only enough CO2 to drop the p/H to 6.5. Keep it there all day.
Use tap and do not add baking soda at all.
That's all you have to do.

I got a JBJ combo regulator, solenoid, needle valve, check valve, &
bubble counter in the mail on Monday and attached it to my 10 lb CO2
tank. The high pressure gage read 800 psi (is this the normal reading
for a full tank?).

Yep

I ran about 12 inches of vinyl tubing (I know this is not ideal, but it
is a temporary solution until I can get some CO2 tubing or some Tygon R-
3603 tubing) to my CO2 reactor

I use silicone, works fine. It's not expensive eitherway so if you
feel better using it, go for it but it's not needed, 100% silicone
works very well.

I started bubbling at one bubble per second. and let it run through the
night. The next morning, my pH had not moved. I kept increasing the
bubble rate until it was going too fast for me to count (5 to 10 bubbles
per second!). After doing this a couple of days, my pH had only lowered
by 0.2 or 0.4 to around 7.2. The pressure on my tank had dropped by 300
psi so I scaled the bubble rate back to one per second. This morning, my
CO2 tank was flat empty.

Make sure you have a seal washer for the reg-tank and also use some
pipe compound or teflon tape on the threads.
Check everything well.

3 bubbles a second should come close to the needed CO2 amount, maybe 4
a second.
Keep the KH at 3.

Set output pressure at 15psi or so.
Make sure the outflow from the reactor leaves the bottom and goes
right into the return from the sump.
Reduce the splash on the over flow box also(raise the water level in
there).
Use spray bars that point downward or are already down along the back
wall of the tank running along the bottom.

Wash plants good, but do not dip for more than a minute at most in a
solution of bleach, some like moss will not survive.

Regards,
Tom Barr