The problem with soldering a large area of copper is it will tarnish with the heat preventing the solder taking to the area. To overcome this I used some paper towel with flux on, wiped a heated area as I went just prior to soldering as this cleans the copper surface so the solder flows easily. This however requires care to avoid burnt fingers and paper towel but works well. To tin solder the parts I placed them on an old stone slab on top of the vice so there is no copper to metal contact that would absorb the heat, the stone gets warm at heat point but has a low thermal transfer rate.