How about prions[0] or something similar? They replicate, and are much simpler and smaller than RNA or DNA based replicators.
* Prions are like falling domino pieces. If you have a lot of standing domino pieces, and one of them falls, it may cause other domino pieces to fall. But they don't create more domino pieces, or standing pieces. They just pull down the pieces that are around. Also, they store no information, they just flip a bit from 0 to 1.
* RNA is like a small pile of glued magnets glued on their side. If you put some glued magnets in a box full of magnets and shake them, they will pick other magnets and create a inverse copy. If the side of the magnets is (magically) sticky, the copy may get glued permanently. After some more shaking, you have two piles of glued magnets moving around and collecting more magnets and making copies. They store information, because the initial pile may be NNSNSNS and the new piles will have the same pattern until there is an error in the copy.
I think the https://en.wikipedia.org/wiki/PAH_world_hypothesis is somewhat similar to your idea. IIUC they don't self reproduce, they just grow in a random order in a pattern. And the proposal is that it 's good to support the RNA bases for a small time to make it easy to build small chains.
[I remember to have read something like that about clay or crystals, but I can't find it now in the article in Wikipedia. Perhaps the idea was abandoned a long time ago.]