Trunk chop again? How tall is it now? Looks like there will be nothing left if you chop lower.
It is usual to chop, wait to see where the new shoots are then complete the cut in an appropriate place near one of the new shoots. Need to let the new shoots grow and harden. Cutting close to soft, new shoots like these you risk breaking them off or having the trunk die back a bit further and take the new shoot. If these grow well you may be able to make the final cut at the end of summer but if the chosen shoots still have green bark leave it until spring I think.
You can leave any lower branches for a while. As Pebble says, lower branches all contribute to the trunk below growing thicker so plenty of low branches is good. The dilemma is how long to leave them. Thick sacrifice branches leave large scars that take some time to heal. Thin branches don't contribute much to the trunk...
