Hi Anthony,
It sounds like you haven't missed anything from your check list. I am sorry to say that it really is the chemicals from the log burner paint.
I have a couple of suggestions. which may or may not work well for you. I have chemical sensitivity, which means getting totally chemical free is essential. I found that airing the house for a week with all doors and windows open was not enough to remove the chemicals totally, and doing this undermines a couple of hours of log burning to heat the house. In our last house we tried lighting the fire at high temperature with all the windows open to burn off what ever the problem was, and it didn't work. The fire was a major contributor to heating the house. We ended up keeping it at minimal temperature to just keep it alight, and that way we avoided the fumes. It doesn't work so well on this new fire, but you could try that. If that does not completely avoid the fumes for you, this technique could be combined with the use of an air purifier. It would need to have a specification which removes chemicals as VOC's, not just dust particles. My purifier has an activated bamboo charcoal filter, but there are other methods of removing toxins from the air. Unfortunately THESE ARE TOXINS. The purifier will also remove toxins which you are not aware of, so a minor bonus.
Why health and safety hasn't yet got around to controlling the substances used on these I do not know, but it really should be in their in tray. I was affected so badly that the second time I went through the room (only access to bedrooms) all my skin was burning. For days I had to wear fabrics over all exposed skin, plus face mask. I enquired about getting the chemicals included in my desensitisation program, and was told that it was too toxic to do this. That means it is very toxic indeed : ( A good air purifier to over match your room size should cope, but do check the spec before buying.

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