I'm going to make a couple of observations here.
First, it seems clear some servers are still running Shroud part 2 and pulling the 4 lieutenants separately instead of together. If you pull them all together to the southwest corner they refuse to die until you pull them apart. This lets you drop them all to zero hitpoints and makes trying to time the damage so all drop together totally irrelevant.
Second, the only way the pull to the southwest fails is when people get too excited and mug the first lieutenant to arrive. The group has to show enough discipline to wait on the slow pokes -- usually fire or the gnoll who stop to cast spells rather than chasing after you and sometimes earth who tries to earthgrab.
Third, I saw dimension door mentioned. Don't load that. If you make a mistake and cast it anyplace other than at the end of part 5 you'll have some dweeb taking the d-door. D-door takes you to the entrance in part 0 and the portal into part 1 closes down after a short timer (under 1 minute).
Unless recently changed its several minutes Dweeb (and it is usually 2 or 3 of them) can't get back to the group. Quest over for them.
It use to be that people wanted d-doors from part 5 because a simple finish out sent them who knows where (usually to the Twelve outside of the Vale)
Much worse, it took you back to the harbor That has been fixed for a long time and finishing out takes you back to Meridia. (Oh.... People want out of part 5 because they don't want to finish the raid so they don't go on timer, they want to loot run the first parts. They stay for part 5 to kill Harry for the rest of the group so anyone wanting to can finish.)
Maybe you know this and have run Shroud on other characters, just not your wizard. So if you do then sorry for the unneeded info. But, if you've never run Shroud and you are also running it on your wizard for the first time ever....
Well, in that case it's info you should have.
Lastly, I've run several times on my wizard and the issue with spell cool downs is really a non-issue. On normal the trogs that pop in part 1 are pretty weak and most groups can melee them if needed (in fact, if they can't you are probably already in trouble). The only thing you really need to look for is portal keepers.
Otherwise, just Wail/FoD/etc. If the mob isn't cleared when the beaters arrive just move on and let them deal with the leftovers.