I put a few ML of vinegar in a bucket with my tap water and that lowered the pH to about a 7.4-7.6 (I forget what it was but it had to be around that).A couple of days, a couple of weeks, no idea until you try it. You would have to check it daily to start with and see how it goes. If you use a lot of peat in a small volume of water, it could drop the KH and pH very quickly, within a day. If you only use a bit of peat in a big container of water, it might take a few weeks, or longer.
You could make a solar still to distill the tap water. Might not work in winter but in warm weather it is free distilled water.
It kept it at that number for about 5 days to a week.
Don't know if peat will do the same in small amounts but worth a try!