My property tax math has a hole in it if family lives there first

I'd rather build something that holds up for years without me fussing over it, so I've been slow about the whole thing. Where it actually stands right now is this.

Detached 700 sq ft unit, bid at $196,000 with a builder I've used before, no allowances, fixed price with two named exclusions (utility upsize and any soils remediation). Permit is approved. I have the cash without borrowing.

The plan was always that my mother-in-law lives in it for two years at no rent, then we rent it at market, which comps say is $1,900 to $2,100 for a new detached unit in my area. So the first 24 months produce zero income and about $2,600 of annual carrying cost in insurance and utilities, plus whatever the tax change is.

The hole. My county reassesses on new construction, and the assessor's own guidance says the new unit gets added to the assessed value at cost, which would put me up somewhere around $2,400 to $3,000 a year in additional property tax on a 1.4% effective rate. Reassessment practice on new construction varies by state and county, so I'm not treating any of this as settled until I get it from the assessor directly. But if the number is real, my first two years are roughly $11,000 of negative carry before a dollar comes in, on top of $196,000.

The alternative I keep circling is charging her a below-market rent, say $600, that covers the carry. That changes the family conversation, and I'm honestly not sure how a below-market family rental gets treated for expense purposes, which is a question for my accountant and not for me.

So the decision is whether the two free years are worth $11,000 of carry, or whether I should be honest that a family arrangement and an income property are two different projects and I'm trying to pay for both with one building. I don't have a clean answer and I'm not in a hurry.