I've been doing this for a while on my tank and healer alt with my random heriocs to save some time.
Queue for random dungeon
When it pops, look for "This dungeon is in progress", if it does not say this it is a fresh instance and drop out of queue and try again.
As a tank, the queue's you get are instant, as a healer on my server, around 1 minute. From my experience, they're usually on the last boss, but if they're not, it still saves time even if one boss is down. Hopefully this is useful to you.