pH up is the wrong way to go .... Chemicals make lots of money for the lfs (that's why it is in the test kit info) but really only gets you into swinging pH.
What you want to do is to find out WHY the pH is dropping, then fix that.
If I understand your tests correctly:
Tap water pH is 7.6.
After sitting in a jug with Prime, the pH drops to 6.8.
Tank pH is slowly dropping to 6.0 over time.
I think the key to understanding why your tap water pH drops is to know its buffering capacity. Testing for GH & KH would be a start. <Alternatively, see if your water co. has water testing results posted .... that would let us know what we have to work with.>
I have recently read that some water co is now stripping hard water of most of the ions by precipitation, creating soft water with very little buffering capacity. Then the water co add NaOH to increase pH (to reduce pipe corrosion), so you end up with water that has high pH but low buffers. <They call this liming the water.> The problem fish keeper face is that the low buffering capacity in the water means the pH is unstable. Then initially high pH in the tap water don't stay that way. You expose that water to atmospheric CO2 & the pH falls. I suspect that is what is happening when you keep your water in the jugs.
Once you get the water in the tank, the pH drops further because fish waste & other decomposing matter creates acids. This can be accounting for your slow drop in the pH over time inside the tank. Your pwc is not helping because the organic acids now is acting as a buffer to hold down the low pH & your change water, having no buffers, will not do much except by diluting the acids.
If low buffering capacity is the cause, the treatment would be adding a buffer to the water. This might be happening in your betta tank ... You might have some carbonate source in that tank (shells, rock, carbonaceous substrate) that is naturally buffering the tank water to 7.6. <To prove that, test the KH in that tank's water. It would be higher than the KH in your tap.>
You have a couple options ... You can maintain your tanks at the low pH of your tap (ie 6.8 after sitting out), and do enough water changes & gravel vacs so that there is not enough waste decomposing in the tank to drive the pH down. As long as the pH is stable, you have no problems. Alternatively, you can add a buffering source (people here like crushed coral) to keep the pH stable, tho at a higher pH of mid 7's. <Just like what appears to be happening in the betta tank.> Because your tank pH is so low, you do not want to do this quickly. I would do that over the course of 2-3 weeks if you were to move the pH from 6.0 to 7.6.
Your best option would really depend on what your inherent buffering capacity of the tap water is ... so I would suggest starting with a KH test.