The Lemmyrinth should also go in the Extra rank. It's a very original concept, but not one that would work among the main ranks.
Alright, finally got some level suggestions to add so far:
2112 - Rhythm of Lem - a nice long level with lots of obstacles. Could work in Picnic.
ccexplore - Every Single One Counts! - this level was meant to demonstrate that you can make your own VGASPEC. However, it also functions like a regular level, and is very interesting because it has a lot of multitasking and you have to save 100%. This can go in the Extra Rank.
Chmera - The Great Migration '06 - perhaps this could be the very first Picnic level? Seems too easy and simple though, but I think it wouldn't hurt to start it simple. Also remove the '06 in the title.
Dullstar - The Ice Palace, The Waffle Express (was not inspired by my name!

), Attack of the Killer Toddlers - all of these were also suggested by Nepster in the
NeoLemmix Community Pack. All three could work in Picnic. Attack of the Killer Todders especially teaches a trick.
Timfoxxy - One of Everything - an excellent and simple one-of-everything level. Place in Hootenanny.
Timballisto - Lemmings on the Roof - has a very clever and hidden solution. Place in Hootenanny.
TOG - Up and Around - this level is the type that teaches you that you don't always have to 100% a level, especially if the save requirement says so. Place in late-Picnic?
TOG - Roller Coaster - a good level that teaches the reverse miner trick. Place in early-Hootenanny.
TOG - Mind the Gap - a level with a very clever solution. Place in mid-Hootenanny.
Tumble Weed - Skill Your Lemmings - a good review of the eight traditional skills. This is different from a skill tutorial level. You already know how the traditional skills work, so no need for tutorials, but a review of how they work and when they should be used is different. A Picnic level.
Tumble Weed - Stairway - uses a lot of clever tricks, one of which is also used in Lemmings Plus I. Tumble Weed included this in his pack of best levels. This belongs in Devious.
Tumble Weed - Multiple Choice - haven't beaten this one, but Tumble Weed included this in his pack of best levels. It works in Armageddon possibly, and I feel Nepster's "Divide and Conquer" (Neutron Star 7) was inspired by this level.
For those who want to make any other suggestions to add, look through the
Lemmix-to-NeoLemmix conversions.
I will go through more level packs and see which levels can be added.