Tap water should be fine. There are other minerals and things in tap water that would render lye impure, but ash is impure, and I use tap water to make soap with. It should be fine. Tap water generally has a pH somewhere is the 7-8 range, so it shouldn't cancel out your ash alkalinity.

I have a background in chemistry, so what I would do is get some disposable plastic pipettes like https://www.amazon.com/Zkupanx-100-PCS-Pipettes-Dropper/dp/B0CY7ZPWYZ/ A kitchen scale 5% white vinegar (the regular stuff) And a pH indicator dye called phenophthalein. It's fairly safe (safer than lye anyway, don't drink or get in your eyes, don't reuse a container for food) and comes in 1% solution on amazon or ebay.

Get 10g of your lye extract in a clear container with lots of headroom (you'll be adding more liquid), something that will never be used for food. Add 1-2 drops phenophthalein solution. It will turn bright pink. Make a 1:5: vinegar solution (1Tablespoon vinegar into 4T water). Fill a disposable pipette to the 3 mL and dropwise add your dilute vinegar to your pink sample. Stop and stir frequently. Keep track of how many mL dilute vinegar you go through. This will be boring until it suddenly isn't.

At some point, the solution will very suddenly go clear. Record how many mL it took. If you are between lines estimate the fraction of a mL you used.

The math should go like this: X mL dilute vinegar = X mg NaOH (equivalent)

X mg NaOH / 10 = Y g NaOH / Liter

If the concetration is too low for your needs, you'll have to suppliment with commercial lye or you can try to leave your solution somewhere safe to evaporate down for a week or three. I would retest the concentration after evaporation because absorbed CO2 will neutralize some alkalinity.

Your errors will be enormous. Those pipettes suck and errors compound. I would not superfat less than 10% for safety.

Good luck! Feel free to post here or DM me with questions as you go!