Actually there is a slight difference between a 28H and 28Z. They have the same floor plan, but the 28H has a different location for the TV (over the dinette), and two narrow windows in the dinette rather than one large one. More like the 29G (but without the bedroom slide).
You can't remove that cabinet because the AC/DC/distribution panel/converter is located in the bottom of that cabinet - at least it is on the 28Z. Well, of course anything is possible, but finding another location and re-cabling the panel would probably cost more in labor than a new 28H is worth.
The best bet is to cut the top off the cabinet and leave the base as a container for the converter. But I am not sure you would have enough room for doing your duty even if you did this.
Also the sink in the bathroom is a "poor man's" black tank flushing system. When you are at the dump station, simply turn on the water to the bathroom sink before dumping. After the first dump, close off the dump valve and let the faucet fill the black tank with clean water. Then at the appropriate time, dump the tank again.
This is perhaps not as effective as a spray nozzle rinse system, but it's better than nothing.
Obviously, practice good RV etiquette and don't do this when there are people waiting to use the dump station.
The only thing that works on a RV is the owner...