After similar experience, my next project will have:

ASHP to UFH.
Bottled Propane (orange cylinders) for instantaneous hot water heater.
Solar PV system exporting to grid.

KISS and avoid inter connecting the heating, DHW and solar with expensive bulky inefficient tanks/stores.

I'm in the process of installing partial A2A ASHP, ducted warm air, with summer cooling as a bonus. I have ST and plenty of PV, so I'm hoping for good overall results.
Given my 35 year old build all over again, I think I'd seriously look at point of use electric water heating and no hot water storage. Underfloor electric for fast response in bathrooms and the like, and ducted A2A heat pump overall, (I'll let you know how successful).
For wow factor and aesthetics a nice big Kachelofen centrally located.

We were in the same boat as you but with new build rather than barn conversion - no mains gas though.

ASHP or GSHP sized appropriately to demand (how do you work out the demand?!) I'll assume with a conversion you are going to require some space heating so UFH - you'll know the usual bits about high radiance areas needing lower flow temps which suits heat pumps, etc. We've good mains pressure and enough space so have a biggish mains pressure DHW tank - both off the ASHP. Downside for me is that the COP drops in winter with an ASHP so it costs more when you need the heat most - bit of a double-whammy - but your situation may vary. We didn't go for a GSHP as our overall heat demand was calculated too low to make it viable.

We've added PV this summer on a S-facing roof - has worked out well as our DHW demand generaly syncs with PV output. No storage though so grid export for what we don't use.

We've 2 wood burning stoves for secondary heating which are overkill 90% of the time. Useful when it was -10 during the day in the winter just gone though.

If I was doing it now or planning for a few years time, I think I'd stick with a heatpump for DHW and UFH but put the PV in from scratch if possible. I'd also leave provision to add grid-tied storage to both smooth out production curves in the summer but also look at importing off-peak electricity in the winter to try and offset the greater demand - octopus energy are developing something like this now I have read.

Max out the solar PV on your East/West roof.

I would then go all electric. Space heating is easy - it's a GSHP (if you have the land available for the pipes) or ASHP. Hot and cold water to the kitchen would be supplied by an instant hot water tap (quooker style) that had a vacuum insulated hot water reservoir. The water in the tank is heated by a lower wattage than a 3kw kettle element, which is great for using your solar. Fit a cold water tap only in a cloakroom (you're only washing your hands after going to the loo and most of the time the water doesn't have time to warm up before you're finished). Maybe buy a tap with a motion sensor to save water. The rest of the house DHW supplied from a tank heated by two immersion heaters, running off excess solar and economy 7. Size the tank on how many bedrooms you have (i.e. potential occupancy) and whether you have a bath fitted (personally I think they're a waste of bathroom space, water and energy but some people seem to like them).

I wouldn't mess about with oil, wood stoves or gas cylinders. Ain't nobody got time for that.