Happy New Year, Unclued, and all the other CHF regulars, and not forgetting our hosts, Ash and Norah. I've yet to solve 30D, and likely won't have any more time on this until some time Monday.
Dylan, the straight answer to your question is that the last cell of PAIK clashes with the first cell of POLYGLOTT. Which isn't a TCD entry, but is part of a list of names.