This is the first expansion that I've largely switched away from my DK. I don't like the changes that they made to blood, and I've put too much time into building a tank to really want to swap to frost or unholy. Blood pretty much went from being a timing-based self-heal class (Cata/Mists, and Warlords to a much lesser extent) that had a strong focus on managing debuffs on enemies, to forcing you to heavily micromanage runic power and a stacking bone shield buff, and...well, still trying to focus on heavy self-heals. Except now you can't do them nearly as often.
To give you a general overview of how DKs's resource management works, you have a rune -> runic power (RP) -> rune cycle. You spend runes, to get runic power, which you spend while your runes recharge. That's how it's always been, that's how it very likely will always be. In Wrath, the rune/RP cycle was very strict, at least as unholy--fuck up once, your cycle is b0rked and your DPS suffers until the next cycle. Cata through Warlords improved that drastically, shuffling around abilities so that you have a bit of wiggle room if you need to do an emergency heal or break off and kill an add, or something like that.
What blood has now is very much like what Wrath had. RP is much harder to get, and bone shields--which used to be a minor defensive buff for unholy players--went from being simply provided to blood to being the primary rotational focus for blood players. This is made tricky by the fact that 1) bone shields are taken away with every melee swing counted against a tank, which is a lot, obviously, and 2) even if the tank doesn't hold threat, the bone shield expires automatically after a while--you have no choice but to maintain it. Since bone shield is responsible for a 16% damage reduction and a 10% haste buff, you really, really need it up at all times.
Another thing that compounds this issue is that RP is now much harder to get. Before, RP generation felt more reliable. There seemed to be more ways that you can get it, including using anti-magic shell (AMS) and soaking magic damage. Now, even AMS barely gets you any RP back, to the point that it may as well not even do it at all. The only way to reliably get RP is to complete a full rune cycle.
That, in turn, significantly hurts our ability to strategically self-heal. Before, death strike--our main self-heal and self-shield ability--was powered by runes. Now, it's powered by RP. Before, we had a ton of ways to get runes back, so if we needed to do a clutch heal, we could pop a cooldown and do it. Now, if need a clutch heal, we need to nuke our rune/RP cycle and there aren't any CDs we can use to enable us to get a quick heal off. Since our healing is timing-based (a base amount, plus 5% of the damage taken in the last 5 seconds) we need to do the nearly-impossible task of lining up our resource generation cycles to damage spikes.
The situation actually feels worse than Wrath did, as we used to have the empower rune weapon available. That was a lovely CD that would give us some RP (20, I think) and reset all of our runes. That would allow us to do what we had to do and then effectively wipe the slate clean and start over. Nowadays, only frost gets that ability.
I raided with my DK when Legion dropped, and things were slightly worse then--we had strong magic mitigation but very little physical mitigation. We got back icebound fortitude (which everyone agrees should have never been removed) back in 7.1. However, the other problems with the class have had a drastic effect. One of the main reasons I didn't pursue raiding after my guild fell apart is simple--nobody in their right mind would want a DK tank. We were being actively rejected from raids because most people simply weren't good enough to get around those issues (even in Mists, where blood tanking was arguably at its peak, people still managed to fuck it up), and because we required a tank healer that could properly read us and know when we're resource starved. Yeah...not a great situation.
I do think that I'm a pretty damn good DK player. I've played them consistently since Wrath and have routinely managed to pull above-average stats, even on weaker specs (in Cata, when frost did noticeably higher DPS than unholy, I had one of the best frost DKs on my realm wonder how in the hell I managed to pull the numbers that I did as unholy), but this is a bit too much. Blood just isn't fun for me to play. Hopefully things turn around in the next expansion. If not, I'll probably go back to DPS.
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Maybe the reason you're not gelling with shaman is because shaman were a lot different when you played them. I'm familiar with how they were before (managing totems placement, etc) but I never played a pre-Mists shaman beyond level 25 or so. Personally, I had a ton of fun on my shaman in recent years (resto/enh in Mists, enh/ele now).
Be careful with DPS classes. When questing they feel pretty tanky in the new 1-60 content, as well as Cata. BC can still truck you if you're not careful, Wrath a bit less so. In Mists, however, enemies would absolutely wreck you if you pulled more than one or two of them at once (might have changed, but I remember the Mists question experience being pretty terrible as DPS when it was current). Warlords and Legion aren't nearly as unforgiving, but you still have to be mindful of what's going on around you, as it should be.
I imagine 6-8 hours for 1-60 would be with full heirlooms, but it's hard to say. Dungeons in particular seem to give quite a bit of experience at those levels, so maybe they're just chaining LFD or something. I haven't done the early game grind in quite a while. You can also upgrade your heirlooms to work through 1-90 or even 1-100 now. It's quite a gold sink, though. I rerolled my pally recently (was going to play with someone, but they abruptly decided that they wanted to play with their new friends instead--sigh), so I might just load up on plate heirlooms and try it for myself.