Floorboards vs. the concrete slab

Hi all,

First timer so be gentle. (plus excuse the long post)

Recently retrenched (if you call 3 months recent), and procrastinating really well by doing some small renos to the house - bathroom upgrade/new kitchen.

This issue relates to the kitchen - dinning area. The previous owner has done "interesting" stuff. I think there are 2 separate additions to the 50's solid brick house. 1) closing in old slate veranda, 2) 2 room brick veneer extension.

The kitchen opens into the closed in veranda. The room is a concrete slab (veranda was slate and seems to just have had a slab of concrete poured on top). Then a hall runs off this (the new extension).

So for flooring the new kitchen/dining room (and the hall as it is "attached"), we have the following situation:

Kitchen - original floorboards unpolished - ripped up bad vinyl tiles (good nick but for trap door I have cut in - can be patched). Island bench to open to dining...
Dining - dubious slab (unsure of thickness - will check). Seems level/dry (haven't checked yet) Sits 5-7 mm higher than floorboards (both kitchen and hall...)
Hall - floorboards - assume they roughly match other ones but different era
We were going to "float floor" the whole area (lift up height from boards with timber underlay), mainly because of the slab. Some "experts" have advised against the floating floor (wet area - though we normally don't shower in kitchen) and "cheap effect" - said tiles the way to go.

Ideally we would polish boards the whole house (bar bedrooms) but the slab stumped us.

Am I mad to think I get someone (concrete cutters??) to drop height of slab (grinding/cutting/shaving) by 20+mm so I could try glue 12mm boards down? Could I get a "close enough" match (is there someway to use the stain/polish to help match)?

Any thoughts/warnings/witty putdowns welcome....

Cheers
P.