It seems to me that you are carrying out a considerable amount of work on a property which requires some specialist knowledge.
While everyone here will do their best to help, (and there's also the free SPAB helpline, which you can use) if this was my house I wouldn't worry too much about what contractors are game to use, I'd give 'em a specification and tell them that's what's required.
Contractors may have their own ideas and those ideas aren't always the most informed where period buildings are concerned.
This is advice based on having worked on period buildings for decades - hire a conservation architect (or a RICS surveyor with conservation expertise) to draw up the specification for you, and oversee the work. Most people will have cratspeople they have worked with in the past too, who they can recommend.
I know this will cost, but in the long term it may save you cash, worry, and get things past planning and, crucially, building control which you may struggle with. It will also mean they are up to date with what works and what doesn't. Yes there may be some people who have had bad experiences, but my view is that it's worth skimping on other things and getting the building right.
If it goes pear shaped with the builders, the professional can get tough.
I take your point but I feel far more able to have the discussions armed with thorough - I don't want to just hand my building over (and I have had very bad experiences in the past when doing so - to an English Heritage listed surveyor!). Also if reed mats can't be used on the exterior, or there ain't no-one around who wants/knows how to use them then there's no point in flagging them up as a possibility. I'm just trying to understand what's possible. Moreover it was my structural surveyor's suggestion to insulate the walls with sheeps wool - which has turned out to be impossible to start with!
I'm not suggesting you hand it over - but a professional with the right expertise (was the structural surveyor a RICS accredited conservation person?) will talk you through the appropriate possibilities.
RIBA has architects accredited in conservation - there are some excellent professionals out there who know what they are doing and can advise accordingly and draw up specifications. As the building is not listed, you could run into Part L problems too with Building Control.
It's not impossible to insulate the walls internally with sheep's wool, but you will have then to construct a wall on top of that and that will lose space and may alter the character of the building considerably.