Those Christmas items are totally compatible, they are just model, texture and item files. You will have to use cheats to obtain those items though, K1R or not.
That is because it is the mod authors who determine whether or not a mod is compatible with K1R or not, the same goes for TSLRCM compatibility.
What mod author's are suppose to do is determine whether or not their mod is compatible with K1R/TSLRCM and check YES or NO depending on the answer. However, not every modder plays or has even heard of K1R so some modder's might just say NO to be on the safe side. If you see mod's totally lacking a K1R compatibility sign that means that the mod was uploaded before K1R and the question as to whether it is compatible or not is best asked here (Like the Christmas mods for example, they didn't include a K1R compatibility sign).
When you say "plethora of HD skins" I assume you are referring to Dark Hope's mods, here is my assumption on why she says her mods aren't compatible with K1R even though they are compatible (They are textures, K1R modifies very few textures). Her first language is Russian and I believe her second language is English, if she plays Kotor with a Russian translation patch that would mean she'd also only play with mods which also offer a Russian translation... and since K1R is an English-Only mod it's a logical conclusion that Dark Hope has never played K1R thus cannot be certain if her mods are even compatible.
As for the Juhani Appearance Overhaul, I do believe that the mod author probably doesn't use K1R hence is why he said it was incompatible. I just checked out the mod and the ONLY thing which raises an eyebrow is upcrystals.2da, but even then, I do believe that since the mod has a TSLPatcher then the mod should be compatible with K1R regardless. 👍