1. If I delete Dawnguard and start it over, will I be able to become a werewolf a third time?
2. Does anybody know if completely restarting Dawnguard will solve my issues with becoming a VL?
The reason it took five minutes to transform(this must be an exaggeration...) is: Your amount of spells you know + powers, shouts, etc + how large your save file may be.
How large is your Vampire's save file? What system are you on?
The more play time, the more scripts build up. The more scripts build-up the longer the delay.
I cannot personally speak for this particular issue as i have not encountered it myself however recently i was suffering from the rather well known dawnguard related c++ crash and i found disabling dawnguard, booting up the save without dawnguard and then saving before reactivating dawnguard to reset it to the start fixed the issue so it is likely worth a shot though i would wait for more peoples opinions. Also due to being a pc user i did use the clearinvalidregistrations command from skse after first disabling which may have affected it. If the issue i faced is anything to go by then a dawnguard reset may be what you are looking for but wait for other people's opinions as well.