My 2 cents
Lessons are the most efficient way to get better with respect to time. At 20 days per year, you don't have a lot of time available to get better. There are ways to make sure that the lessons you pay for are taught by instructors who will give you great value for your money spent, but these methods require that you do more work than walk up to a ski school desk and whip out your credit card. One way you can get lessons for free is to get yourself videotaped and ask the Epic community for coaching. You may get more than what you pay for doing this, but in person coaching from a qualified coach will still be a more effective use of your time.
If you have the capability to learn by watching, you can pick out people on the trails you're skiing and do what they do. The younger you are, the easier this is. It's even better if you can follow a better skier to ski their line exactly. Spend more time hanging out with better skiers and you will undoubtedly get better through osmosis. As others have noted, learning this way does not guarantee that you will reach expert ability. However, it is possible.
Books and videos can also help you progress faster than learning on your own, but they are not an effective substitute for in person coaching either. Some books that can help:
Skiing and the Art of Carving - Ellen Post Foster
Tactics for All Mountain Skiing - Chris Fellows
The All Mountain Skier - R. Mark Elling
Ski the Whole Mountain - Eric and Rob DesLauriers
The Athletic Skier - Warren Witherell & David Evrard
There are tons of videos available here on Epic, Youtube and all over the web. The Canadian instructor videos
and the Italian instructor videos
(see the "oro" links) are my favorites. There are a few commercial high end "how to" videos available, but none that I will recommend here on Epic. If you search through other threads on Epic, you'll find the links and understand why.
Don't overlook the value of Internet forums like Epic to add to your understanding of skiing from books, videos and personal experience. It may take time to separate the wheat from the chaff, but it is a free resource and can provide more detailed information than a book or video can.
Getting new boots and having your alignment checked may help you progress faster. Find a reputable shop and take their advice. Gear can
make a significant difference in your ability to reach higher levels of ability. Whether or not getting new boots and/or having alignment work done will help you enough to be worth your investment in time and money is a crap shoot without more information and could still be a crap shoot with more information.
Skiing is an athletic activity. Several of the books mentioned above have fitness sections. The most often overlooked fitness areas related to high level skiing are over developed quads versus hamstrings (a contributing factor to ACL injuries), core muscle strengthening (e.g. abdominals and back muscles) and balance skill improvement. Finding highly qualified fitness coaching can be even more problematic than finding highly qualified ski coaching. Self coaching for fitness can be as risky as self coaching for skiing.
Good luck on your quest.