OK that’s not an option then - unless you have a neighbour with high alkalinity tap water who doesn’t mind you popping round every so often with a Jerry can!Tap water and well water are one and the same. There is no alternative.
Other options:
Mash using base malt and light coloured grains, add your dark grains at the end of the mash. Dark grains add acidity but if you add them at the end of the mash pretty much all the conversion is already done.
Use bicarbonate of soda to add alkalinity, though add a lot and your beer will taste flinty or minerally.
Buy some bottled water that has high alkalinity, this might be relatively expensive.
A novel approach I’ve seen on-line, and is supported in a book I have that’s all about water (really!), is this one….
Take a corny keg and half fill it with your water (you could alternatively use a plastic fizzy drink bottle and carbonation cap). Add precipitate of chalk at maybe 10g/l. Pressurise the keg/bottle with CO2 to about 20-30psi. Every time you walk past it give it a shake. Carbonate will try to maintain equilibrium with dissolved CO2 which means it will dissolve more quickly when under pressure with CO2. When you want some high alkalinity water take some from your keg and shake the CO2 out to give you a saturated carbonate solution. This process mimics what happens in nature but is far quicker. You might want to buy a Salifert Alkalinity test kit so you know what the alkalinity is so you can add the right amount.