Hey! As long as you read continuity across all grounds (strips and Pixelblaze, which will also be the ground of the output expander), the data line will have the necessary reference ground. You shouldn’t need additional ground connections.
On long runs, a few things can happen. One is that if the ground conductor is undersized, it might have a resistance that starts to drop significant voltage at times of high current. This would raise the effective reference ground voltage at the strip end relative to ground at Pixelblaze, which I’m assuming is physically near the power supply and not the strips. If there’s not enough difference between data’s high (Vdd) and Gnd at the strip, they won’t work. From V=IR, a small resistance in the main Gnd wire such as .1 ohms, if providing 10A (167 LEDs full white), would raise the reference ground at the strip by 1 whole volt. The data wire’s signal differential is now 4V instead of 5. I’m not sure if adding an additional smaller Gnd wire in this case would help much; my intuition is that it wouldn’t.
Another thing is that the length can start to act as an antenna, which can induce enough voltage at frequencies that interfere. We’ve talked about using twisted pair (gnd-data) and differential transceivers if this becomes the problem.
A potential issue I see here, is that you may end up with an appreciable amount of ground current running through the PB/expander from the PS to strips 2 & 3, or even between strips 2 & 3, if the ground connection from the PS to those two strips is poor or the ground wire gauge is undersized.