Your sequencing is right and year one is the worst year. The servicer runs an annual analysis, computes the new monthly base from the projected disbursements, then either spreads the shortage over twelve months or lets it be paid as a lump sum. Ask the servicer in writing which options they offer on that loan, because it varies by servicer and by investor guidelines, and a lump-sum payoff of the shortage is usually accepted.
Whether the reassessment actually lands the way you modeled depends entirely on your state and county, since some states reassess on transfer and others only on new construction or periodic cycles, and the loss of an owner-occupancy or homestead exemption is a separate line from the reassessment itself. Get the current exemption amount and the reassessment rule from the assessor's office rather than from a comp.
A prefund does work mechanically, since you can send funds to be applied to escrow, and lenders accept payments from third parties routinely. The exposure isn't the money, it's the paper trail. The insurance change is the loudest signal in this whole transaction: a new policy with a different named insured, a landlord form instead of an owner-occupied form, and possibly a new agent all get reported to the lender by the carrier. That's a far more common trigger for a due-on-sale inquiry than a payment arriving from an unfamiliar account.
Also model the tax bill timing. If the reassessment bills in a cycle where the escrow analysis has already run, you can get a disbursement larger than the account holds, the servicer advances it, and now you're carrying an advance plus the shortage spread. On a 313 dollar gross spread before vacancy and repairs, that year is negative and you should know by how much before you commit.
