I find it strange that similar shower units can be so different, I think the answer may be to fit a power shower, but I've not looked into this other than a power shower needs a cold and hot water supply.
If I decided to go for a power shower could this be fed from the hot tap that feeds the bathroom sink, via the immersion tank? It may solve the problem for me, although the hot flow is poor compred to the mains cold feed.
Stephen.