Spliced LED Strips with Pre-Fab Controller
For anyone coming across this question in the future:
I ended up doing as I intended -- soldering two strips end to end (cutting one strip near the end on the metal contacts, and running small jumper wires to attach the end of this strip to the beginning of the next)!

Only difference is that I used a different controller than what I posted here -- I ended up going with the ALITOVE LED WiFi Controller SP108E, because it works with app on phone to control via bluetooth (or WiFi I guess)...and it worked!! The ALITOVE controller had an initialization step of setting how many LEDs are in the strip, and I simply set the correct number of LEDs in the spliced-together two strips, and it recognized all of them such that patterns accurately pass over the splice like it wasn't even there!

Thanks for help.