As it has been noted, the Highland Park is not an Islay, but an Islands (Orkney island, to be exact). The Islands are in the very northern end of Scotland, while the Islays are from the islands in the southwestern region.
like you, I was wanting to try something a bit peatier/smokier, and the HP 12yr was highly recommended. The bottle I purchased came with an 18yr sampler bottle, and did not break the bank.
While it was indeed peatier than anything I had tasted previously, I didn't really get the "smoky" flavoring that some characterize it with. However, it did have a nice sweet flavoring, and I did enjoy it quite a bit. I would highly recommend the HP 12yr. Great whisky!
For a much stronger Islay flavor, I went with the Bowmore Legend. Now THAT has some gusto! Definite 'smokiness' and VERY peaty! So much so, that I might have this bottle around for a LONG time to come!
If you want to try something vastly different than either the Glenlivet or Highland Park, try the Aberlour 12yr. It is a very reasonably priced malt with a GREAT flavor! It is double-casked in sherry casks, which not only give it a darker color, but a LOT of flavor has been soaked up in the whisky.
It is one of my favorites...
Others I would recommend on your longer list include the Dalmore, Cragganmore, and Balvenie 12yr (Doublewood).