That is a very good question for us forumites to opinionate/bloviate over. First though, a round of applause for those out in the field arduously and riskily obtaining important field data that cannot be had from armchair remote sensing!
The significance of ocean waters warming and eroding ice shelf underside is not limited to Petermann as similar processes may be operative at Nioghalvfjerdsfjorden and indeed under Antarctic ice shelves. Petermann, while not a tour destination, is relatively more accessible and could provide early model guidance to the others.
Both aspects of ocean interaction with ice shelf are non-intuitive: it is not a matter of waiting centuries for local water to warm. Oceans have indeed warmed slightly but the issue here is pre-existing warmer currents advancing to new places, already possessing ample heat to melt ice sheet undersides.
Secondly, the induced bottom melting is not uniformly planar but by all accounts quite pronounced just down from the grounding line and elsewhere channelizing the ice underside in a complex fashion driven by daily and seasonal fjord circulation and intertwined temperature, salinity and density profiles.
Five drill holes is a decent but not extravagant number. These could conceivably be guided in their placement or augmented by one-time casts through 'whirlpools' and other direct routes through the ice which we could conceivably locate beforehand. These holes have some interest in that they collect regional melt water and inject it locally on top of the subsurface water column. However one-off casts at random tidal stages and season pale in comparison to steady time series and the effort could be a huge resource waster.
I'm supposing hot water drilling (no ice cores, no gravity sediment) with an instrumented wire frozen in (rather than moorings), periodically reporting from a top package to a satellite, not betting the farm on relocation and one-time retrieval. However placed, these strings will drift down their flow line some 3-4 km over the lifetime of the project. Thus, to the extent the bathymetry is known to resolution, these could be placed over bedrock channels or set instead to drift over troughs and sills.
Thermisters and conductivity give density and perhaps changes in ice depth overhead. I don't have a sense whether currents will be measured or are even disentanglable from positional drift via topside GPS (or more simply, corner radar reflectors).
Given five drill sites, it seems like the first decision is allocation between horizontal versus flowline transects. I would discard both edges as not representative nor safe to drill; these might add up to 7-8% of the width. It wouldn't make sense to drill too close to the calving front either.
The benefits of a staggered hole line escapes me, so that leaves a 3+3 configuration of horizontal plus flowline, either T or +. For now, I would say 3 across fairly near the grounding line and 2 down the flowline from the northeasternmost hole, subject to revisiting the bedrock radar and what is known already about shelf bottom channeling and fjord circuation