I find it amusing that my own experience is 'okay, what do I want to bolt onto an iridium band'... that was literally my first thought when I saw that, and didn't even consider any combination that didn't include an iridium band. Because an Iridium Band is already, effectively, three rings for the price of one... a glow ring, a magnet ring, and a ruby ring.
My initial response was nearly identical as well... iridium band + burglar's ring = win. You generally kill monsters because you want their drops, burglar's ring lets you do that faster. So, that's one ring down. What's the other one going to be? And I had several ideas:
* Ruby Ring. 10% more damage is 10% more better. Especially since my Galaxy Hammer already has 3x Rubies on it for even more damage. Let's see if we can get this puppy to one-shot eels, if not the new mobs in the volcano that drop shards. Because needing half as many swings to kill them means half as much time spent killing them so your grinding of the shards goes that much faster.
* Napalm Ring. Much for the same reason you did. The lulz/meme factor of mining through blowing mobs up.
* Vampiric Ring. I haven't put a prismatic shard property on my hammer yet, so I valued it slightly higher, but the simple fact that you CAN (should you sink enough prismatics into it to roll the one you want) massively devalues this option, unless they stack in which case it may well obviate needing much in the way of food, depending on your play style.
* Crabshell Ring. +5 Defense is pretty potent, and I think probably better in the long run for more casual players than Vampiric, because it's a lot of damage you simply aren't taking, arguably more damage than the vampiric ring can heal off, depending on how often you are being hit vs how much damage you are dishing out. Keep in mind that the space boots, prior to this update the undisputed champion of footware, only had +4 defense, this would be more than doubling your defense rating.
* Immunity Band. +4 to Immunity is legit huge. As of the current update, it reduces the chances of getting hit by debuffs, and apparently that is all debuffs now not just the shadow shaman curse, by 10% per level of Immunity. Space Boots has a +4, the new Cinderclown Boots is +5. So add this +4 to that and you get an 80% to 90% odds of NOT getting debuffed. Heck, the Mermaid Boots have a +8, so you would literally never be able to be debuffed at all when wearing them.
Any of these paired with an iridium band would probably work well. I don't like the 'proc' rings like the warrior's band or yoba's band because they feel too inconsistent to me.