I've tried some similar "imagining" when it comes to thinking about how Void Caller might impact deck-building. My conclusion is that without the actual Void Caller and other new cards it doesn't quite work out, and as a result, neither does Void Terror and many associated Demons. The effect simply cannot be replaced, and without it, those picks just don't make sense.
With this deck, I think I probably wouldn't bother with Shadowflame at all. Best use for it is probably on your Azure Drake to do 5 damage to everything or combo with PO, and, obviously, that's quite "heavy" as you would put it.
Particularly with Shadowflame, Siphon Soul and PO, I agree with taking DG out for AC, or something along those lines.
My own Demon build (which does a lot better than I first thought it would, albeit I don't use it in Ranked), not accounting for Void Caller or other future cards, keep in mind I personally have a much more Control oriented playstyle, so it's very different from yours:
2x Mortal Coil
2x Amani Berserker
2x Faerie Dragon
2x Shadow Bolt
2x Earth Ring Farseer
2x Pit Lord
2x Sen'Jin Sheildmasta
2x Bane of Doom
2x Siphon Soul
2x Argent Commander
1x Ragnaros the Firelord
Note, I do not consider this a "good" deck, but it isn't strictly "bad" either, and there are a LOT of cards that I put in there because it would be "fun." Primarily Bane of Doom, Deathwing, and Pit Lord. Also, I too do not have a Leeroy, so Ragnaros is my replacement (it makes sense in my mind, stop judging me). If I had Leeroy I'd replace Rag obviously and probably put Faceless in place of Deathwing.
For me, what I've experienced is this:
1. It's really nice to have 3+ AoE. Deathwing doesn't do as nice a job as I'd like as a third AoE, though it can win games sometimes and people generally don't expect it. None the less, I think in my "serious" decks I'll stick with 2x Hellfire and 1-2x Shadowflame, provided they aren't rush decks (in which case I'll only use 1-2 Hellfire, which can be nice as a finisher at least), or Zoo (where I just won't use any).
2. I think Demonfire, Shadow Bolt, Mortal Coil, and Siphon Soul is more than enough targeted removal. Drain Life (or bane of Doom) can be useful sometimes, but as has been discussed in this thread, you generally want things that are "always" useful. With AC, Hellfire, and such supplementing it, it's that much less of an issue to include additional removal, and you can safely cut back on others (most commonly Demonfire and Shadow Bolt). From my perspective, the only things Drain Life are good for are to gain life (I'd rather use a Voodoo Doctor) and Spell-based Face damage (which isn't a great decktype currently, but has it's moments).
3. I still really wish they'd remove Blood Imp from the pool on Bane of Doom. I think that would have made it a much better pick.
4. I haven't really felt like Siphon Soul is slacking, even with this more midrange build (compared to Handloc).
5. I miss Azure Drake for making best use of Mortal Coil and Shadowbolt.
From playing with Azure Drake and Hellfire in my Handlock, I can say it can be sometimes annoying, but it's generally not too much of an issue. If I'm using it, it's usually either to slow down Aggro (meaning my Azure Drake is either not out yet or already pretty injured anyway), or it's a finishing blow to more valuable late-game minions/the enemy Hero. I can also say from playing both decks that Earthen Ring can help take the sting out of Hellfire's downside, by healing surviving minions and/or yourself. It can suck to Hellfire after throwing out a Twilight Drake or Tazdingo the previous turn, but a little shamanic love can go a long way to help.
Based on your build, it felt like you were going for a more aggro-intensive bent than I did. The result of this is that I feel like you're a little spell-heavy, and again the Doomguards just don't fit well with the spells you do have. If you ditch the Void Terrors and Doomguards, you can also ditch the Sense Demons, as it won't get you anything consistently important. Demonfire might also become questionable, but you've still got 4 decent buff targets, so it's really dependent on whether you want more minions or not. If playing with a more Aggro focus, more minions seems like the better choice. You could replace them with Owls to help you get past large taunts with your Arcane Golem/Leeroy or AC. Presence of Silence could also mitigate the need for Siphon Soul, and so on.
Again, it makes spells look bad, but I think a large part of it is what you're using them for and how effective you can use them. For my midrange-ish "Demon" deck, the Demonfire can be useful to buff demons, but with my playstyle it can also mean slowing down Aggro, or setting up for Mortal Coil or Bane, etc. So with my deck I feel like it's more valuable.
Sort of how I look at things. I've also toyed a bit with Frost Elementals and Corruption, but I haven't made anything that I think would be worth sharing deck-wise with those.