Can't think of a good way around it. RaidCooldowns only knows the cooldowns for the class running it, since they're broadcasted. _Display has to know the cooldowns for everything it's tracking regardless of class.
Any chance of getting each bar to show the name of the spell used, instead of just the spell icon?
Charname - spellname - time
Came here to post the same thing actually, or even just a tooltip on mouseover if thats easier? Being a tank 99% of the gaming time I don't know what half some of the spells other classes use which makes it harder. I do ofc recognise the things I want to know (misdirect CD on hunters, fear wards on priests n bloodlust) but it would just make it easier if I could glance at the bar and know what spell it was without having to think for 10secs in the middle of a boss encounter.. :)
(edit, also what Kerecha just put but instead in my case only have it enabled when in a group.. I don't particulary need to know when another random warrior in shat pops Bez Rage for example ;) )