move homestead exemption from SFH to a "house hack" quadplex?

[Bill McCasky]

I'm moving into 1 unit of a quadplex that I'm purchasing via a pocket listing, closing this week.

Is it better for me to leave the homestead exemption on my SFH (appraised at $225k) or move it to the new quadplex (appraised at $425k) as of 2017.

I'm thinking i should leave it on the SFH that has a higher valuation, as I will only get the HS exemption on 1/4 of the quad, correct? This would be the best fiscal decision as far as I can tell, but looking for confirmation.

Follow up questions - Will the county reappraise the new quad right away? Can they find out sales price from a pocket listing if its not on MLS?

This is travis county, texas.