Hiya Prelude,
I can tell you that whatever the pH of the water, even if it's got a lot of lime in it, the peat will be way too acidic to make a difference, by far. In no uncertain terms, you
need to add dolomite lime, otherwise you'll get poor results.
If you look at any commercial potting medium that uses peat or peat moss, you'll see that they always add lime to sweeten the pH. It's not optional, it's a necessity. I really don't know how to emphasize the importance of this enough. I can guarantee that your results using peat moss without adding lime will be poor since it's just not suitable on it's own.
The tap water will not lower the pH enough since it would probably take years to get enough calcium deposit from the tap water to raise the pH to the 6.5 level. If the tap water lime was enough then manufacturers would not routinely add lime to their peat-based composts. Trust me, it's not some unusual gardening practice. It's common practice all throughout the gardening world. When you make the change I'm certain you'll never look back.
I'll tell you what, if you don't believe how much of a difference it makes, why not just take several cuttings and lime a couple of pots of peat moss, but not the rest. Then assess just how much of a difference it makes. But if you do any research you'll find that every source will tell you to add lime (whether it be dolomite lime or garden lime - get dolomite if you can) to peat moss to raise the pH as it's far too acidic. The pH of peat moss from Canada from example (which is probably what you are using) is about 4.5. The idea pH sweet spot from cannabis is about 6.5-6.8, so that means your peat moss is
one hundred times more acidic than the ideal pH cannabis enjoys (the pH scale is logarithmic)! This massive pH difference simply cannot be corrected by the lime in tap water, unfortunately. If the pH of the medium is too low, you will have problems with nutrient lockout (could explain some of the issues you've been having).
Adding dolomite lime is also important since it contains abundant amounts of both calcium (Ca) and magnesium (Mg), both of which cannabis needs in relatively large amounts. Because sufficient calcium levels often is missing from nutrients, adding dolomite lime to your medium will prevent issues with Ca/Mg deficiencies from ever happening. The dolomite lime adds lots of both Mg and Ca, unlike normal garden lime and acts as a buffer, usually not raising the pH above 7, and so is much much better than the garden lime you normally find in garden centres/ nurseries.
Thanks for the comment re my pics and good luck with your growing mate. I hope I've managed to convince you, but if not, hopefully you'll find out yourself how much of a difference adding dolomite to peat moss actually makes