For the in progress dungeons, I have run out of time once in Stone Vigil and that's due to needing a healer as well and one didn't queue until we only had 10 minutes left. Otherwise, I have run out of time four times. I have never run out of time on a pug run, but I also do less of these since I usually group with the same ppl, especially while I was leveling.
Once on Quarn - We really needed to figure out the first boss (still hate that boss), the second time we ran it after time expired we got it and finished the dungeon easy.
Second time in Cutter's Cry - Again, first boss, beat it with 6 minutes left with the healer kite strat. Next time got it down and beat it with plenty of time.
Third time was on the last story dungeon. We were watching the cutscenes and wiped on Ultima Weapon twice. Cutscenes are super long for the time they give you on that dungeon.
Last one was on Demon Wall, we were a little undergeared so it was a super pain. Now he is super easy and its actually a cool fight.
Even with these, I think the timers are fine. If it takes you longer to learn a fight while leveling then its totally fine to have to try again. There is no where that says you should be able to beat a dungeon on your first try every time. If you are running out of time on as many dungeons as you are saying than something is wrong. You sound like you have horrible luck, but in reality there really is enough time to learn the current dungeons, wipe a few times, and replace members for most groups.