Look for places to taste stuff and if you really like it buy a bottle or take notes and look for it in a shop. If it is a single cask be sure to get all the details on the label you can. While almost all of the distilleries are importing things to the US, there are always specific bottlings for local markets. And distilleries often have distillery only bottlings. I suspect most of the independent single cask bottlings are local markets only as well, so you could look for those. Note Cadenheads no longer makes it to the US, but they have a lot of good stuff and usually you can taste in their shops if you can find one. If you can make it to a good whisky shop that would be the best place to get something in line with your tastes and also get reasonable information on whether it is available in the states (although more often and not they may not know). Two personal Islay favorites of mine that didn't make it to the US are Ardbeg Almost There and Renaissance. Those were limited editions but you might find one around at a still reasonable price (I noted in a recent trip to London that all the "uncommon" Ardbegs are going up significnatly in price). And since you like Laphroaig, there is a "Triple Wood" out that I believe is for duty-free only. I have a bottle but have not tried it so I cannot comment. There are also some Highland Park duty free only bottlings, but I don't know the details.
As for bringing it back, the way I understand it is that there really is no limit as far as the federal government is concerned. You are allowed 1 liter duty free, and anything above that is supposed to be declared. I think it is around $3-4 per liter extra. But the problem here is that the laws of the state in which you enter the US override the federal laws. In Georgia, for example, the maximum you can bring in appears to be one gallon, and the first half gallon is supposed to be duty free. I think the next half is relatively cheap, like for federal. But it took me a while to find this out, and the TSA people at the airport seemed pretty clueless about it, so I suspect that you could be subject to the whims of whatever customs officer happens to be working in whatever city you land. I've heard customs officers say they bring in 2 liters and don't worry about it, so who knows.
Shipping from a shop or distillery to your US address is technically not "legal". There is probably a proper way to do it through an importer, but who knows what that would cost and how long it would sit in customs. There are on occasion shops in the UK who will ship to the US, but you assume all the risk. Apparently from what I have heard the odds are pretty good your stuff will come through. And you can always try shipping to yourself. I'm not sure what the regulations are for that.