Thanks for all the tips. I tried turning the table on its axis already. Sure, this then provides a pair of lateral (X) and a pair of (in-line, in Y) slots. So that’s some progress.
I could then mount the vice ‘sideways’ so that the jaws are in line in Y and rotate the whole table around the pillar to get the drill axis above the right spot in the work. Not ideal but at least not impossible. It’s not ideal because the drill axis would describe an arc over the work clamped in the vice as I’m trying to line it up by rotating the table around the pillar, which is awkward. Also not ideal because on my ‘cheap’ drill press there’s a certain amount of play in the table’s collar around the pillar and tightening it up to start drilling causes a certain amount of movement of the table relative to the drill axis.
I could also add packing work in the vice to get the desired drilling centre under the drill axis, but that is probably the most inconvenient option of all.
Using milling-style clamps to clamp onto the web of the vice would allow a certain amount of wiggle room for aligning the work under the drill axis, and perhaps if I make some dedicated clamps this would be the best option.