For one year you will have a weird hybrid homestead cap.
Your cap next year should be this years appraised value plus 10% of this years value plus the market value of only the new additions.
As far as what you should do this year, it could be a very complicated question, yes you theoretically should be able to lower the value to the value of the property as it existed on January 1st, but because of your homestead exemption, that could theoretically alter the appraisal district's viewpoint of what should be assessed at market value as the new additions not subject to the homestead cap the next year and create a fight over that.
For example, if you convince an ARB to decide your lot is only land value this year, then next year the CAD will interpret that 100% of the improvement value will not be subject to the cap because it's new additions over last years land only.
However if you dont aggressively go for it to be valued as land only, and they view your construction as a partial addition/renovation and not a complete rebuild, maybe only the added 2000 new square feet will be fully not subject to the cap rather than all 4100 SF not being subject to the cap.