Wouldn’t recommend using a solder paste unless you have a dedicated stencil suited for the size and pitch of the USB pads - If you do have such a stencil, then 63/37 Leaded solder paste can be used, just buy the paste from a dedicated electronic distributor such as Mouser, Digikey TME etc etc… and avoid the stuff frrom china, apply paste on direct heat stencil on USB pads etc and bring to reflow temp, when solidified remove stencil and follow my steps (above and in the linked topic) to properly install the USB connector.
If you don’t have a dedicated stencil, then use 63/37 leaded solder wire (from above distributors) and tin the pads (pillows 
) and follow my instructions here -Need to vent and question about charge port replacement - #6 by Severence
The install should be a two step process and not a one shot process.
Does it do the following on your USB current meter
0.4A then after a few seconds drop to 0.0A then back to 0.4A or is it a constant 0.4A?
It’s because the battery/power source isn’t your primary issue