This is probably still pretty borderline, but might be acceptable...
Fit 7.5kW electric showers. Fit pressure reducing valves before each shower to limit the flow to the shower to eg 1 bar to minimise the pressure changes in the flow, ensure it's hot enough - and make sure the plumber fits a high capacity pipe to provide the main feed for all the showers.
(2 x 7.5 x 100%) + (3 x 7.5 x 25%) = 20kW / 230 = 86amps
That is going to take you above the 100amps, but as the load is only likely to be short duration - 10-15 minutes, and it's only actually likely to be 5 showers in total during any given period as it's one person per room (i assume), I'd think there's a reasonable case for thinking this could be acceptable. Even at 15 minute showers, that's still only 9.375kWh in total for the 5 showers, spread over half an hour would give an average power draw for that half hour of 18.75kW or 81Amps, which matches quite well with the diversity calcs.
A 100Amp fuse will allow 150Amps to flow for half an hour or so without blowing, or 170Amps for 10 minutes (ish) so I can't really see that there's much danger of that from the showers while being used normally... if I'm reading the curves right.
A lot depends on the other loads in the building though, if there's electric heating, cooking etc then it's probably not going to work.
Interested to see what others would say to this suggestion though, as I deal with this stuff from the generation end of the spectrum mostly, and volt drop is my main limitation rather than current usually. In a previous life I did used to spec generator capacities for festival sites though, which involved similar calculations and considerations.