The matter of tinning the cups, placing the jumpers, and landing the cable, are all going to come down to experience and personal preference. For me, I'd work out the length and bend of the jumpers (using solid 22ga or 24ga bus wire), and fabricate as many as needed. Then I'd tin one cup of each pair being jumped, and tack the jumper in place. Solder the other end and re-flow the solder on the first end if needed. The right amount of solder flowed correctly will leave a shiny, concave joint. Applying a very small amount of solder to a clean iron tip before soldering will aid in the transfer of heat, and will flow the solder into the joint more readily.
You may choose to land the cable's conductors at the same time as you solder the second end of the jumper. It's up to you to determine what works best for you. Experiment. You can also land them on the jumper itself - hook the end or just tack it along side. Cables should be properly strain relieved so as not to rely on the mechanical strength of the solder joint, so it doesn't really matter which way you choose as far as that goes.
It's essential that the wire be nice and tidy before you tin it, and that it be positioned so that it wants to relax into the cup as you solder. Trying to force a wire into position with the iron, or by pushing on the wire, etc., is a mistake that will often end up with a frayed end, loose strands, or melted insulation.
As far as the phantom problem goes... here is no need to worry about the chassis ground connections. If you have properly wired the hot, cold, and shield wires, then everything should be fine. You may have been left with the impression, after watching that Neutrik video, that it's OK to plug a mic into a TRS patch point (jack) as he did... it's not OK if you have phantom switched on! If you tried this, you may have blown the phantom supply
Try plugging a mic into your pre directly with an XLR cable to check that the phantom is still working OK. If the phantom is confirmed to be working then check your connections with a meter to make sure that you have continuity and no shorts.
BTW, to follow convention - solder T-2, R-3, S-1
Not to discourage you, but personally, I would not use this connector for a mic input with phantom power.