Now that you got me on the UCC track, I see that under UCC 2-207(1) if the writing had quantity on it and there was no conditional upon acceptance of the new price term, then we would have an acceptance. I don't believe these parties are merchants, so the price term would be a proposal for adddition to the K.
I think we also could find a K here under 2-207(3), if it's found that the writings aren't sufficient. Reggie went out and bought the materials and wanted to begin building.
I believe the Statute of Frauds would be met to, if not in the writings then under subsection 3(c).
Let me know if I'm off.