Some rough hints at the levels that will be repeated. Specifically, here's the count of how many in each style, and from what ranks.
Breather (easier versions): 0 Sky, 2 Circuit, 2 Martian, 3 Lab :: 0 Timid, 1 Dodgy, 3 Rough, 3 Fierce
Rehash (harder versions): 1 Sky, 3 Circuit, 1 Martian, 2 Lab :: 5 Timid, 2 Dodgy, 0 Rough, 0 Fierce
Also - unlike with the LPII Bonus Pack, the repeats will not nessecerially be in the same order the levels were. eg: If there was a repeat of Timid 11, it would not nessecerially come before a repeat of Timid 14.
EDIT: The "unconfirmed" lab level, the solution I had in mind works but cannot be backroute-proofed without heavily modifying the level; and since I want to not modify the levels *at all*, it's a no-go. I updated the count to reflect that, as well as a newly-added level to the set - still one gap to fill.
You may be wondering how these are going to work with Dodgy, given that the solutions were usually already somewhat puzzley - one case is a gimmick level that no longer has a gimmick in repeat form; the other is an entirely different (and in my opinion, harder) solution with a fairly different skillset.
Also, the fifth rank will be called "Party" and will mostly consist of levels that use combinations of gimmicks. The other two gimmicks from LPIII (the surviving bombers and Lazy+Exhaustion combo (it's practically treated as a single gimmick as far as Lemmings Plus is concerned, even though technically it's a combination of two)) will be used in at least one secret level each; and may also be used as part of some of the combos. The Party levels might also use LPII gimmicks too. This also means that the Moonwalk and Teamwork levels will be purely one gimmick each; no combinations there.