I"ve got a old 444 also. Some previous owner repowered it with a Kohler. The issue I have is that the set screws for the variable pulley don"t seem to hold well. Every once in awhile when hydraulic pressure is applied to the variable speed cylinder it pushes the cylinder off the shaft, which then bends up or breaks the rotating fitting on the end of the cylinder, and they are not cheap. Did you have this problem and did your three new set screws help or solve this?
Without going into a long story about the backyard repower the PO did and all the misalignments which have beat the heck out of the crank and thrust bearings in the engine (I"ve fixed these issues), I"m probably looking at a new engine in the future. Have you been happy with the Briggs? Any particular reason you decided on the Briggs and not the Kohler (I see Small Engine Warehouse offers both for the 500).
I"m like you, I don"t have much invested in the machine, but it works.