I can see a good way of using the checkerboard vs barbs: if the barbs swarm into the holes, push the principes forward a bit and compress the barbarians (against the men behind them), so they can't get enough room to swing their swords. If the barbs didn't swarm the holes, just switch between hastati and principes pushing forward/falling back in good order. The risk is of course that the entire line will be fighting at the same time at some points, and that the barbs will skirmish: threatening to enter the gap, then falling back, repeatedly, to tire the principes who would go backwards and forwards a lot (with heavier armor than the barbs wear).
But perhaps it's possible to counter this as well, by alternating between pushing the principes forward, then pushing them beyond the hastati, and the enemies in the gap would be compressed by a following (short) hastati advance. Or the principes/hastati formations could be deep enough to be able to present a deep enough front while still having men behind them move sideways into the gaps and hit the enemy flank harder than the enemy can hit the roman flanks.
In any case, by default the checkerboard doesn't give you any greater outflanking penalty than the opponent because where you are flanked, he is also flanked. Only if one side has equipment or training better suited to this kind of situation, would there be any difference. My guess is that the romans (and the samnites which they copied the checkerboard from) had made sure their equipment and training made them superior at this kind of fighting.
Anyway, I've had some fun experimenting with schemes of this type in EB

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