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Variant that doesn't rely on potentially undefined behavior of asking "repeat" to repeat before the beginning:

cHJpbnQgMApwcmludCAyCnByaW50IDAKcHJpbnQgMgpwcmludCAwCnJlcGVhdCAzIDIKcHJpbnQgMgpyZXBlYXQgMyAyCnByaW50IDIKcmVwZWF0IDMgMgo=

Good eye.

Also, https://github.com/wgreenberg/quine.zip/blob/gh-pages/test/i...

Sure, but LZ doesn't necessarily allow that.

How do you use these strings?

They're base64. Feed them to "base64 -d" on Linux, or one of the many base64 decoders on the web. See https://en.wikipedia.org/wiki/Base64

This is the shortest one of the solutions so far. Wonder if it's the shortest possible? (Other than empty = empty)

Hm. Well, it was the first quine I arrived at. No special effort was made to make it short.

Yes. It is the unique shortest possible solution if you allow for a repeat at the beginning. OTOH if you disallow starting with a REPEAT, the shortest is length 10.

Another similar to your idea: cmVwZWF0IDQgMw0KcHJpbnQgMg0KcmVwZWF0IDQgMw0KcHJpbnQgMg0KcmVwZWF0IDQgMw0KcHJpbnQgMg==