I think the issue is that the CO has certain guidelines that they must follow, and you don't know what those guidelines are, or what buzzwords to say. Without that, you're flying blind, so to speak, as you don't know what will count as a good decision and what would be bad. That's where a local architect experienced in listed buildings would be able to help. As far as I can guess from your post, you're proposing to destroy historic fabric (i.e. cutting a hole to put the flue in). The CO's job is to preserve historic fabric, so they've suggested a way that you can get what you want while preserving historic fabric. I think that whether or not historic fabric is preserved is a very concrete issue, whereas the aesthetic tastes of people in 2012 is a very subjective issue. You thus have the rather wooly argument of 'but it looks better', while they have the concrete argument of 'it destroys historic fabric'. (If you think about the historic background to preservation of historic buildings in the UK, I believe a lot of what we have today is the result of William Morris and co's reaction against the Victorian tendancy to 'conserve' everything by making it more how they thought it should have looked, and less how it actually did look.) An architect might be able to argue that the historic fabric will be better preserved by the inclusion of a flue within the church, as it will make it so much warmer and take it out of the danger of woodworm etc.
Our house is very different to yours - it's a 16th century timber-framed farmhouse in East Anglia, but also with an oil-fired boiler which is getting on a bit. Our first winter was grim - my elderly dad ate Christmas dinner with a bobble hat on his head. In terms of heating, we don't yet have insulation in the vast majority of the house - that's this year's big project. I'm in hopes that will cut down the bills massively. We looked at GSHP but we have the original floors in some of the rooms, so don't think underfloor heating is suitable. Our neighbours have a wood pellet boiler, but I can't work out any way to incorporate the wood pellet storage and the boiler on our house without it looking very odd. We'll probably just replace with another oil fired boiler, sadly.
We have all the dull things - secondary glazing, thick woollen curtains (those are great - you can literally feel the cold air falling out at you when you draw them back in the morning), rugs on the brick floors, draft proofing and curtains on the doors, etc. Rumour has it that our COs are tentatively dabbling in conservation double glazing, so in 5 or 6 years we may be able to move to double glazing in the vast majority of the house. Blocking up the fireplaces and putting in wood-burning stoves made quite a difference. I have plans to put draught excluders around the doors to the sitting room too.
I think that radiators are crucial, though. We now have a sophisticated zone-controlled heating system which means that each room is heated to the appropriate temperature for the time of day. That alone made a terrific difference straight away. It meant we could afford to heat the house, because it wasn't a case that either the entire house was hot or cold. Instead, we now have all the rooms warmed up in sequence to match our daily routine. (It means it's freezing if you get up unexpectedly early, but that's a minor drawback).
I should also say that after the first winter we got used to living at a lower temperature, and didn't ever need to go back to having a house as warm as we were used to - but then I'm typing this with a rug around my shoulders, and we do go in for thermal undies and even thermal slippers. I'm happy to use 18 degrees as 'warm' and 16 as 'cool but okay for rooms you're not sitting in'. DH likes it a degree warmer. We put it up to 'normal' temperatures when relatives come to stay.
I can imagine a converted church must be freezing. At least we're south facing and have big windows all along our south face - although our floors mean we stay comparatively cool in hot weather.
BTW, I should say that we have a flue not dissimilar to what I think you're proposing and I reckon it looks foul, it annoys me every time I look at the house. Can't say whether or not what your CO is suggesting would look any better!
That's a really long post but I do sympathise with you. Meanwhile, are you members of a fuel co-op to get best oil prices?