I have hiked the GR 20 as well and I don't think the Kungsleden is more crowded. I just don't like trendy trails – on the northern Kungsleden you will see a whole lot of Germans on a "survival tour" equipped with bowie knives and axes… I am a little bit exaggerating and I am German myself….
I have hiked extensively over Scandinavia and I would suggest the following trips:
Sörmlandsleden: This is a very long trail in Southern Sweden around Linköping area. Check out: http://www.sormlandsleden.se
This trail is not "exciting" in the sense of a Haute Route – it is mainly through a lot of forests but also hitting a lot of very beautiful lakes. If you want to see the variety of Sweden, I would at least hike a part of that trail. Sweden is not all the barren beauty of the Sarek, but also lots of forests and nice villages.
Southern Kungsleden: Much easier to get to and landscapewise much similar to the Northern Kungsleden. You could start at Storlien in Sweden and then hike over to Röros in Norway sampling a bit of the very scenic Femundsmarka (the whole trail is along the border). I did that in one week.
But really instead of messing with the Kungsleden I would rather suggest two hiking areas in Norway. Distancewise they are even shorter from Uppsala than the Northern Kungsleden:
Jotunheimen: This is the very best of hiking in whole Scandinavia in my opion. It is a national park with an extensive trail and hut system – there are a lot of Norwegians but it is not as overrun as the Kungsleden. This is one of the most mountaineous (does that word exist?) areas in Scandinavia and it is breathtakingly beautiful! I did a East-West-traverse and a North-South traverse, each taking me about a week. Easy to get to and my absolute favourite.
Hardangervidda: This is a huge high plateau and again a national park. Very easy to get to even with train. This has a very harsh beauty (no trees at all, no mountains, just a plateau). Again I did a East-West-traverse and a North-South traverse, each taking me about a week. This is my second favourite.
Both Jotunheimen (meaning the home of the giants) and Hardangervidda a parks with a trail system so you can make up your own route from daytrips to week-long trips. The DNT (Norwegian hiking organization) has overview maps for planning purposes.
On the Norwegian train system there is a bargain called "minipriser" (meaning mini prices). If you book the train trip ahead on the internet you can get them that way really, really cheap – and believe me, there is not much that is cheap in Scandinavia…..
Don't hesitate to ask if you have more questions – I like to promote hiking in Europe.
Christine