So many questions :LOL: tough call tho, making do with what you have may be cheaper but more expensive in the long run if its not got the power to do the job..
Slightly confused by your electrical calculations they worry me :LOL:
Regardless if you use 5v or 12v leds you will need to work out the max current that the entire strip can draw at max brightness (Current - in amps) and pick a power supply above that rating - for extra protection you can fuse the main supply to the leds so the strip cannot draw more than the max amount.
You could use a 12v supply on a 5v strip but you'd need to drop the voltage down but the supply still needs to have the required Ampage to power the strips in the first place, you can also use the same supply to power the pi but you would need to add an extra 3amp on top of what the led strip requires so your other power supply's may not be up to the job.
Once you have the correct power supply you can worry about the volt drops, each time you DO NOT use a soldered joint or add in a bad soldered joint or any sort of connector you run the risk of adding in points of failure, weak points or bad connections etc and that is what causes the actual volt drop in the circuit.
Example would be a 40 strand wire - 39 strands are cut and only 1 remains intact, If you put a meter across that you may see next to no resistance but put a bulb at the other end and try to power it and its a different story - The current simply cant get to it fast enough to light it, same scenario with twisted wires, clip on connectors etc, it may not happen straight away but it's bad practice and can cause more problems later on as metal expands and contracts with heat so it could cause intermittent problems.
So ideally solder any joints and add in additional power supply/earth connections to the strips to prevent volt drops across the circuit, regardless if they are 5v or 12v leds
Don't use the pi as the only earth point for the leds, that's a accident waiting to happen, you need to earth the led strip back to the psu and tap into it for the earth on the pi GPIO
Hope that helps you in someway, Good Luck