Looking back at your OP...I think you're confusing alkilinity and bicarb. They're not the same and I doubt your pool water test kit will test bicarb. Bicarb is HCO3, alkilinity is CaCO3. High bicarb, alkilinity and pH are related but not always directly...I don't think. Acid reduces all.
I use Brunwater to adjust mash pH. I check the water prior to adjustment, plug that reading into brunwater and make my additions, then a few minutes into the mash I check my pH. Usually shoot for 5.4 mash pH and 5.2 kettle pH for lagers. Lager yeasts don't tend to lower pH during fermentation as much as ale yeasts.
According to my last Ward Labs water report my well water bicarb is 139 and pH 7.8. Last brew day my meter said the pH was 7.1. Brunwater said my lactic acid addition brought the mash pH to 5.42, bicarb and alkilinity both to negative numbers. This was for a pilsner. In darker beers the acidity of the grain helps reduce the pH.
For Pilsners I find it's all about adding more lactic acid than you may feel comfortable with but the Pilsen(the city) water profile is very very soft and I'm happy with how mine are turning out.
Read the water knowledge again in regards to bicarb. I learn something every time I read it. Also you could search on here for threads where Martin Brungard has commented on bicarb in brewing water.
In the end do what works for you. Brew a few test batches with all three waters, spring, distilled, treated tap...decide which works best for you then minimize the aggravation and cost of purchased water where ever you can. Just my 2 cents...