A difficult question I know, but can any expert out there recommend a
"dream" boiler-type/storage tank/heat exchanger so that I could start
to put together a system specification that has a good chance of
working?

Your main issue here is choosing a boiler that can maintain a low flow
temperature for the underfloor for efficiency reasons, whilst giving a high
temperature to the hot water system and radiators. I believe the MAN
Micromat can be set up to do this, and Andy Hall may be able to advise on
such a system.

Otherwise, you'll just need to set a high temperature and rely on the
underfloor thermostatic mixing valve to produce a low return temperature,
which may be enough for reasonable efficiency anyway. Should the Micromat's
price put you off, I'm very happy with my Worcester-Bosch Greenstar 28HE,
which is a mid-high end boiler at a much lower price.

For frequent baths and superlative multiple showers, install either an
unvented hot water cylinder (i.e. Heatrae-Sadia Megaflo) or a heat bank
system (i.e. DPS Pandora). If having it installed professionally, you'll
find more installers familiar with the unvented cylinders. However, for DIY
installation, the heat bank will be an easier job, although will require a
higher flow temperature than is optimal.

Your ion exchange water softener should be a high flow type, such as a
Kinetico 2020c HF. Whatever you buy should be metered, not timed.

Christian.