My assumption was the each individual led chip will re-transmit the signal to the next led, which in effect will turn the 3.3v signal into a 5v signal between the 1st and subsequent leds.
The power lines do sustain voltage drop over longer sections, so you'll want to add extra power every few meters.
Right, that is exactly how it works. If your signal to the first IC isn't perfect, and it isn't with a 3.3v signal, you can end up with incorrect colors or shifted patterns.
As you add more LEDs you have a greater chance of one at the end not lighting up or having incorrect colors throughout the string.
0.7 * 5v == 3.5v, and 3.3 < 3.5. You're out of spec for the part and can't expect it to work reliably.
The power lines do sustain voltage drop over longer sections, so you'll want to add extra power every few meters.