For raids with little to no 372s from the previous raid tier, you may want to leave all DPS at the bottom in Phase 1 and send only a tank and healer to the top.

Even if your healers and tanks are competent as you say, the key to this fight is really strong DPS, at least in a 10-man. We went in last night for the first time on Beth'tilac and were unable to keep the adds controlled after her second Smoldering Devastation in phase 1 due to not enough DPS. As a result, we changed our strategy and tried keeping all of the DPS down below (not sending someone up in phase 1 to join the tank and healer) so we could at least get to phase 2 and work on it. We were able to comfortably control the adds in phase 1 with that extra person helping, but when we started phase 2, she was at 100% and we wiped due to her Frenzy reaching 25 stacks or so.

If the other guides and videos aren't helping you, here are some things you might try, from an "average" 10 man guild that got our first kill last night.

One person is enough to kill all of the spinners, but we found it was better to have more people killing them to get them dead faster and ease healer mana. People with long ramp-up times and who struggle with target switching can stay on the drones, but the rest of your ranged should kill spinners if there are any spinners up. This includes the spinners that have not been taunted down, in case that wasn't obvious.
Spinners, when they are down, continue casting their random fireballs, and also melee their top threat target. It's not a ton of melee damage (1.5k hit on plate to 5k crit on cloth, every 1.5 seconds or so) but due to the number of targets, it may be difficult for your ground tank to pick them all up. Try not to pull down more than you need. We had our hunter and holy paladin pull down the first two, and the hunter pulled the third as well 8 seconds later. Prioritize the ones that are running free over those that are being tanked, if applicable.
Taking the dones to a specific, pre-determined location was not helpful for us. Instead, we used a "donut" where the ranged dps and healers are in the donut hole in the center of the room (you can mark this location with a raid marker), receiving AOE heals, and the drone is tanked on the donut, opposite the current batch of spiderlings. Just be sure never to face the drone towards the raid. Mmm, donut.
Beth'tilac's consume ability restores 10% of her health and has a 100 yard range. This means if there are ANY spiderlings alive when she comes down, she will fully heal and the rest of the encounter will be needlessly difficult.
The tricky part is this: assuming you don't allow any drones to drain her energy, there will be a wave of spiderlings about the same time that Beth'tilac begins her third smoldering devastation. At that time it's imperative that all DPS with any AOE capability whatsoever kill all spiderlings. None of the videos or guides I read seem to mention this (though I'm sure there are some that do), but it was extremely important for us.
In phase 2, our healers could keep us up until about 30 stacks of Frenzy. If you're going over that, either Beth is healing or you don't have enough DPS. If you're dying long before that, your healers aren't able to keep up (note that this doesn't necessarily mean the healers are failing).
It's not absolutely necessary to alternate tanks in the traditional sense. Since Widow's Kiss's duration is shorter than its cooldown, for us it worked better to have one "main" tank and one "soak" tank just for Widow's Kiss. If one of your tanks is a druid, consider having him or her soak the debuff and just DPS in cat form while he/she has the Widow's Kiss.
We found it was helpful to save heroism/bloodlust for about 40% so that it fully benefits healers as well as dps, since that's the most challenging part of the fight to heal, and it also happens to be approaching your dps' execute phase.

My guilds first kill on this happened with Beth'tilac starting the burn phase at 100% health... Somewhat to our surprise, we just healed a lot, burned her down, and all was fine. 1 person dead if I remember. This on 25man, Normal.

After a few wipes--We downed her tonight! As a hunter, I was easily able to handle all the spawning Cinderweb Spiderlings with the Concussive Barrage, Rapid Killing, Rapid Recuperation, and Bombardment talents. The first slows the spiderlings while the last three provide enough focus regeneration to allow for Multi-Shot spamming (without a need for Steady Shot).

Having one character focus on the spiderling adds allowed for the other two ground DPS to focus on the Cinderweb Drone and Cinderweb Spinners making the ground team's job easily manageable. Another tip I have for hunters--if you pop Deterrence when you first engage the boss (while waiting for the first Cinderweb Spinners to come) you can prevent damage done by Ember Flare to help conserve healer mana.

Also note, though it is considerably easy for one DPS to focus down the Spiderlings in phase 1, I do suggest the raid help AoE down any remaining Cinderweb Spiderlings before phase 2 to ensure no Cinderweb Spiderlings are Consumed by Beth'tilac when she lands.

j ai bien regarder en haut en plus du tank et d un heal il faut 2 dps comme ca la phase en haut dure moins longtemps apparement