Well, just looking at one tiny timespan in the logs, I think I can give you a few pointers to both problems. (IMO, so much overheal and not enough heals when they count are probably related issues.) Looking at the short period in time on the last pull just before you died in the Whirling Corruption (using WoL because of better death events):
First some observations. The first whirling corruption (WC) tick hits at [01:11:41.700]. You got 2 ticks from the Weapon just before that (used Displacer Beast way too late). You did not use Barkskin although it was off CD. You did NOT cast Wild Growth during WC (in fact, your last WG hots ended [01:11:34.936], so it must have been off CD). You did not bloom your shroom, and the log shows that there were only pets inside your Efflo during WC. You only had 2-3 Rejuvs on the raid when WC started. You cast your Tranquility way too late (as WC was almost over) so it couldn't save those players that were low (as yourself). According to the log, you did nothing for 2 seconds during WC (before starting to cats Tranq).
So, what would I conclude from those facts?
1. You were completely unprepared for that Whirling Corruption. This is the moment in the fight where healing counts, when you need to shine as a druid. You want 6-10 Rejuvs on the raid, use WG the moment it starts (SotF really shines here), have full mushrooms well positioned, and if you use tranq, use it as soon as WC starts (maybe even with SotF).
2. This is an indication to why you overheal so much, and heal too little when it's necessary. You need to focus on the moments when your healing is important, and prepare for that. Garrosh hc is an extremely dull fight for healers most of the time, and only has some extreme moments. On our last Garrosh hc kill, I cast 54 Wrath and 27 Moonfires, because of so much down time. Use that time to prepare for the intense moments.
3. From your shroom comments, it sounds like you are not using them enough. A lot of the fight is done stacked, and a lot of the damage comes in bursts - perfect for shrooms. You want FULLY LOADED shrooms for every Star Impact (P1), weapon (P1 if stacked tactics), and WC. Also use it during the intermission (once fully loaded, once near the end).
4. Make better use of your defensive cooldowns and HS.
5. I'd really like to know what you did during that WC phase, not casting any spells for 2s:
[01:11:41.700] Garrosh Hellscream Whirling Corruption Rowin 89008
[01:11:41.735] Rowin casts Rejuvenation on Rowin
[01:11:42.097] Garrosh Hellscream Whirling Corruption Rowin 86188
[01:11:42.509] Garrosh Hellscream Whirling Corruption Rowin 82562
[01:11:43.306] Garrosh Hellscream Whirling Corruption Rowin 89178
[01:11:43.733] Garrosh Hellscream Whirling Corruption Rowin 91177
[01:11:44.167] Garrosh Hellscream Whirling Corruption Rowin 92922
[01:11:44.531] Garrosh Hellscream Whirling Corruption Rowin 96886
[01:11:44.539] Rowin casts Tranquility
[01:11:45.302] Garrosh Hellscream Whirling Corruption Rowin 96090
[01:11:45.738] Garrosh Hellscream Whirling Corruption Rowin 54917 (O: 41092)
So, I would say there is definitely room for improvement here. Maybe also for the raid tactics (did you know in advance where you would be standing, to place your shroom? Why was there no healing CD up during the whole WC?)
You can try to get a better feeling for the boss. Fraps yourself on some attempts, and later watch yourself healing and ask yourself how you could have healed more during intense moments. Make sure you always now exactly what is going to happen next in the fight and prepare for that.
Since my analysis is only based on a small portion of the log, not everything is necessarily true. I'm open for feedback to discuss certain things in more detail. I hope I could help a bit, though.
Edit: If you log out in Resto, I'll gladly have a look at your character again