Hey there 
I have an NIC cage too, mine is 2 deep, 5 wide and 3 high with two levels. I want to make it 4 high but keep the two levels and just add a couple of ledges. It houses a pair of bunnies, 2.5kg and 3kg. I originally built it just for one bunn, my 3.2kg boy Bandit.
Mine love the second level and it’s where they spend all their time lounging. They love hopping up and down the steps as well. 5 grids high would be very high, and unless you are very tall would be tough to manage/clean. But 4 high is certainly still practical, I would avoid 6 grids high, and for me personally I would add an extra grid onto the length before going 5 grids high.
As for my flooring, mine is vinyl flooring stuck down onto plywood. It can be a bit slippery for jumping under bunny feet, but you can get textured ones. It’s also very easy to clean. I put fleece over the top, and clip it onto the floor with bulldog clips on the top level, and anchor it under the litter box on the bottom level so that it doesn’t slide around too much. The flooring on my steps is foam puzzle mat tiles cut to size. Some bunnies will chew these.
For door latches, I use dog leash style clips. Here’s some pics of my set up 
Cage and play area.

Closer one of cage.

Clips I use to hold fleece on upper level.

Clips that I use for the top and front cage doors.

Flooring on the steps.
