As suggested earlier, I figured that a better result might be obtained by painting with aqueous charcoal suspension ("charcoal paint") , and that has indeed proved to be the case, as should be apparent from what follows.
The lump charcoal was first reduced to a powder with a hammer, and then a little water added to the powder. That did not give a satisfactory "paint", with a lot of charcoal floating on top. As soon as a few drops of detergent were added (washing-up liquid) a relatively homogenous paste was obtained that could easily be applied to fabric with a brush as if painting.
The following pictures should be self-explanatory:
Next experiment? It is said that the image is not formed on the cellulose fibres, but on a surface coating of starch, the latter having been used as an aid to weaving:
Evidence for this is that the image can apparently be stripped off physically with adhesive tape (which is certainly not the case for scorched cotton) or reduced chemically with diimide, N2H2.
So the next step is to repeat the experiments with a starch-coated fabric. It's my guess that scorching will occur more readily with starch, which is chemically more reactive alpha-linked glucan, than with cellulose (beta-linked glucan), the latter having more extensive crystallinity due to multiple intermolecular hydrogen bonding interactions. If scorching can be achieved quickly, then it may indeed be possible to strip off a superficial scorched layer from underlying cellulose, simulating more closely the characteristics of the Shroud. I shall have to think of an authentic (historically credible) source of starch. It certainly won't be potato starch!