Why not try to
acclimate your Cardinals to 7.2 and leave your pH stay there?
If you decide to tamper with it, beware that you are getting into a high level of maintenance demand. I do it, and I love it.
So if you still want to get to 6.8 with natural means I know these three:
A) Get some Peat Fiber (I love Fluval's). I don't recommend the peat pellets unless you have a canister. If your KH is at or close to 5.5dKH use at most 1/3 of the bag (that's what I needed for my 29gal bow before I added CO2) but remember to keep an eye on you KH readings! If the KH reaches 2.5 be extra careful, consider removing some or most of the peat. Use a bit less if your KH is around 4, a bit more if above 6.5.
B) Also consider
DIY CO2 or an entry level CO2 system. One or two 2L bottles should drop your pH from 7.2 to 6.8 easily. Add an airstone that works only at night. I wouldn't combine peat with CO2 for drops as low as you look to attain.
C) Another way of lowering pH naturally: Use Indian Almond Tree Leaves (I managed to drop pH from 7.8 to 7.2 in a 145gal tank this way). Remember to replace the leaves every two or three weeks.
Pepetj
Santo Domingo