Laguvulin is honestly kind of middle of the pack for "iodine-ish" (like the original poster, I can relate to some skepticism with these labels) smokey whiskies. If that put you off, and you like Highland Park, I'd say that you'd probably be better off focusing on lighter, subtler whiskies.
The cheaper versions of that would be, for example, a Redbreast 12 (Irish) or a Glenmorangie 10. The only Highland Park that I have sitting around is an 18 year old, and I just compared them to that (again, the nice thing about whiskies is that you can put a few drops in a glass for comparison), and while they both have a little less to them than the 18 year old, they're also less than half the price. If you're feeling like branching over to the fruitier side, something like a Glendrodach 15 would be worth trying. It's not soo far off from the others, but tastes a bit sweeter and is a bit more complex.
If you're committed to smokey, non-iodine-y whiskies, Talisker is good, as noted. Maybe a Bowmore 12 (a little sweeter), or, if you find it, Ardmore or a Ben Riach. But again, it sounds more like your tastes go away from the smokey stuff to subtler whiskies.
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A thing I'll note for the uninitiated here is that another nice feature of whisky is that there are literally only dozens of distilleries. There are something like 80 in Scotland. For a whisky nerd it's entirely possible to have a good 1/2 to 1/3 of them on a reasonably sized shelf. And since bottles take several years to go off, you really can have a huge percentage of the total range represented in a moderate whisky nerd's collection.
I expected the iodine to be a subtle taste note. Then I woke up in the middle of the night with an intense iodine aftertaste that made me feel like I was in the hospital.
However, I love wood smoke, so I'm intrigued enough to keep at it. I'm trying out some non-smokey whiskies too; I had a glass of Macallan 12 that I enjoyed quite a bit.
You can also put marbles into them to restore the volume, but I don't bother. I've only once had a bottle that went far off (meaning too much of the alcohol evaporated out), and I'd kept it with only 2-ish shots in it for probably a year and a half. So normally after I get down to about the last quarter bottle, I try to finish them within a couple months, and that's done me well.
For me, Laphroaig Quarter Cask was also the first Whisky I bought. I kept it around for a long time (maybe 2 years) because I did not want to "waste" it too quickly.
The last few glasses I drank were really disappointing compared to the initial fanstastic glasses. I can't describe the tastes, but it was simply not good anymore. When too much air gets into the bottle, the Whisky can oxidize, changing its taste (usually for the worse).
From what I've seen, most people using preservation techniques aren't worried so much about alcohol loss as various other molecules getting oxidized, changing the flavor profiles they spent a lot of money for. (I don't have enough experience to say how valid that is, but it's certainly a problem for wine.)
The cheaper versions of that would be, for example, a Redbreast 12 (Irish) or a Glenmorangie 10. The only Highland Park that I have sitting around is an 18 year old, and I just compared them to that (again, the nice thing about whiskies is that you can put a few drops in a glass for comparison), and while they both have a little less to them than the 18 year old, they're also less than half the price. If you're feeling like branching over to the fruitier side, something like a Glendrodach 15 would be worth trying. It's not soo far off from the others, but tastes a bit sweeter and is a bit more complex.
If you're committed to smokey, non-iodine-y whiskies, Talisker is good, as noted. Maybe a Bowmore 12 (a little sweeter), or, if you find it, Ardmore or a Ben Riach. But again, it sounds more like your tastes go away from the smokey stuff to subtler whiskies.
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A thing I'll note for the uninitiated here is that another nice feature of whisky is that there are literally only dozens of distilleries. There are something like 80 in Scotland. For a whisky nerd it's entirely possible to have a good 1/2 to 1/3 of them on a reasonably sized shelf. And since bottles take several years to go off, you really can have a huge percentage of the total range represented in a moderate whisky nerd's collection.