Do you want to run steam, or just heat water?
The 3/8 copper will go around a 4" pipe pretty well. Just go slow in the beginning so you make sure you don't kink it. After the first wrap is on, it will go like clock work. I wouldn't use solder on the connections. I am with Kladue on the silver braze. On my boiler I managed to liquify a soldered joint that was outside my boiler.
Here is a shot of mine where I merged the 4 1/4" tubes into a 1/2" fitting. You just need a bigger fitting. This is silver brazed and I am glad it is.