As already mentioned, I'd avoid lifting any boards. They are glued for a reason, after you've lifted them and replaced them, they'll squeak, and you'll regret it.
If the ceiling can be skimmed after, then holes from below is the easiest, typically I use 100mm dia holes. Keep all the plugs and put them back in the same holes, with a bit of timber batten to support them.
If you want to avoid ceiling damage, then I'm with holes from the floor above using one of the cutters. Yes a kit costs £50 but a good part of that is the steel plates (£4 each), which you'll need.
I sometimes use a right angle drill that can fit through the 100mm access hole. That way, I only need an access hole every other joist. But there is the risk of hitting existing cables & pipes in the voids you can't see, so try to work out where existing cables and pipes run first. If you've already cut the downlight holes, that gives you some clues as to what is in there.
Sometimes you can be lucky and find existing holes & cables. A recent kitchen 8 downlight job, one row of lights was almost over a run of cables, I could use the existing lighting feed from the switch to pull in a new cable between several lights positions. A good cable rod set with magnet & chain is sometimes very handy.