Green cabomba may not like the harder water, but the rest will be fine.
Go ahead and try the cabomba, but don't spend a lot of money on it.
Oh, and I think I know the gravel that you have... It was sold as "Aquarium Gravel" right?
I would say that your tap water is 7.8, but the water coming fresh from the tap has a lot of CO2... CO2 lowers ph, so as an experiment, get a bucket of tap water, run an airstone in it for about 10 minutes. The PH should raise.
If you have DW and the CO2 is the problem, it will probably lower a little bit (depending on the wood.)
May want to boil it first to release the majority of the tannins... I placed a relatively large piece of driftwood in one tank tand the PH went from 7.0 to 5.9 in two days... Oddly enough the PH stabilised at 6.4.... *shrug*