Sql Server 2014 IO Resource Governor
Do you know what pages are getting the latches? DBCC heavily uses tempdb as @ShawnMelton was alluding. Have you considered that tempdb contention could be the source of your pagelatches?  You should be able to investigate that with sp_whoisactive if you aren't already. How many data files do you have for tempdb? It sounds like you've only got one, try bumping it up to 4 and increase in intervals of 4 as needed, though 8 is often enough for most systems and many suggest starting with that number of data files. You'll also want to ensure the files are equally sized. You can also look at this post which has lots of info and links to reduce the impact of dbcc including a post from Paul Randall on running DBCC on a VLDB which might be helpful.