The currently ongoing researches will continue as normal, so feel free to respec everything.
I did it recently, asked in zone, respec-ed, checked the researches: all good.
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At least on PS4 it seems like you have to respec back into the number of research points you had. For example I had respec'd from researching 3 items to 2 items. When I later on put it back to 3 items I suddenly had one item that finished. It might have been coincidence but I think that 3rd item was hanging out in limbo until I put it back up to 3.
From my experience (and checking last night) if you respect, your items will continue to research but at the slow rate they would have if you didn't put those points in. If you put the points back in, the time drives down to match.
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I actually had my last 3 nirn items in woodworking finish without the research time points spent. It takes significantly longer, but it does work. You won't lose the number of items you're researching.