Is it sufficient to just break the data line?
I would think that with Vpp being applied to all chips at the same time, you would be clocking in random data to the chips that aren't being programed, since the data pin is floating and Vpp is on.

Even if you use a Pull-Up/Down, you're still clocking in all 0's or all 1's. Don't know what that would do?

Disconnecting both DAT and CLK with pull-downs on each, might do the trick.

Of course, the easiest way is to have separate Vpp's.
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