I'm a DIYer rather than a pro, and I personally find it far less time consuming (and easier) to tile on a flat surface, and not too difficult to fill holes with plaster, so I'd favour that approach - and probably even have a go myself.
Normally I'm pants at plastering, but if its being covered in tiles the plaster doesn't have to be smooth and nice looking - just flat (particularly without any convex bulges). It does help if you have sound plaster either side of your holes, though, as you can scrape a long bit of straight wood across the patches before they set, to level them to the height of the sound plaster.
Something like 'one coat' or 'patching' plaster could give you a reasonable working time, deal with varying depths and a make fairly hard/tough surface to tile onto. I'd also wet the holes with a sponge or something so that the moisture doesn't instantly get sucked out of the wet plaster when you first put it in, and so cause the plaster not to stick properly.
But if any professionals say otherwise go with them - this just works for me as someone who couldn't plaster a normal wall to save their life - it may not be the 'best' approach.
(BTW, I understand that you can 'sometimes' also tile over existing tiles, if the originals are flat, soundly fixed and if the total thickness of tile layers wouldn't be too heavy for the supporting plaster/wall/adhesive. But personally I've never tried it - when i might have done the extra thickness was inconvenient or the existing tiles weren't quite where I wanted the new ones etc. and it sounds like thats not an option in your case anyway)
Cheers
kev