I am puzzled by your terminology. Replication implies high-fidelity copying of information. That is what some crystals (e.g. barium ferrites) can do. It is an "information bearing replicating crystal". So, what exactly are you asking for? and why are the polytypic layer structures in barium ferrites not it?
You ask for splitting. However, one of the key insights in this area is that you can have evolution-without splitting - via "vegetative reproduction":
http://originoflife.net/vegetative_reproduction/
For some plant evolution, you don't need splitting, only growth. Much the same is true for some "2D" crystals too.
Not that splitting is terribly demanding. Make anything big enough and it will break up - if only under its own weight. The real issue is whether the split introduces mutations that lead to a meltdown. That is a potential problem for 1D crystals - but 2D ones don't depend on splitting - and if there are splits there are still likely to be operational viable growth fronts after the split.
The clay theory is just not going to be taken seriously until someone has a population of clay "organisms" replicating away in a lab and then starts running long-term evolution experiments on them like Lenski is doing with bacteria.
No-one else can make life from primitive materials yet either - this requirement strikes against every OOL theory equally.
To recap, the main reason for thinking Crystalline Ancestry is true is because clay mineral crystals actually replicate patterns of reasonable size with high fidelity under plausible pre-biotic conditions (and this is the #1 requirement for any evolving system) - whereas no other pre-biotically plausible structure has been demonstrated to do so.
However, it's a reasonable request to want to see evolution based on the theory in the lab. Growing many clays in the lab is terribly difficult - and often takes forever - but success there would be interesting. However, much of the existing work has been done with "found" natural clays. They seem to be a more obvious focus - in some respects.
Please read the post before voting on the comments, as this is a game where voting works differently.
Warning: the comments section of this post will look odd. The most reasonable comments will have lots of negative karma. Do not be alarmed, it's all part of the plan. In order to participate in this game you should disable any viewing threshold for negatively voted comments.
Here's an irrationalist game meant to quickly collect a pool of controversial ideas for people to debate and assess. It kinda relies on people being honest and not being nitpickers, but it might be fun.
Write a comment reply to this post describing a belief you think has a reasonable chance of being true relative to the the beliefs of other Less Wrong folk. Jot down a proposition and a rough probability estimate or qualitative description, like 'fairly confident'.
Example (not my true belief): "The U.S. government was directly responsible for financing the September 11th terrorist attacks. Very confident. (~95%)."
If you post a belief, you have to vote on the beliefs of all other comments. Voting works like this: if you basically agree with the comment, vote the comment down. If you basically disagree with the comment, vote the comment up. What 'basically' means here is intuitive; instead of using a precise mathy scoring system, just make a guess. In my view, if their stated probability is 99.9% and your degree of belief is 90%, that merits an upvote: it's a pretty big difference of opinion. If they're at 99.9% and you're at 99.5%, it could go either way. If you're genuinely unsure whether or not you basically agree with them, you can pass on voting (but try not to). Vote up if you think they are either overconfident or underconfident in their belief: any disagreement is valid disagreement.
That's the spirit of the game, but some more qualifications and rules follow.
If the proposition in a comment isn't incredibly precise, use your best interpretation. If you really have to pick nits for whatever reason, say so in a comment reply.
The more upvotes you get, the more irrational Less Wrong perceives your belief to be. Which means that if you have a large amount of Less Wrong karma and can still get lots of upvotes on your crazy beliefs then you will get lots of smart people to take your weird ideas a little more seriously.
Some poor soul is going to come along and post "I believe in God". Don't pick nits and say "Well in a a Tegmark multiverse there is definitely a universe exactly like ours where some sort of god rules over us..." and downvote it. That's cheating. You better upvote the guy. For just this post, get over your desire to upvote rationality. For this game, we reward perceived irrationality.
Try to be precise in your propositions. Saying "I believe in God. 99% sure." isn't informative because we don't quite know which God you're talking about. A deist god? The Christian God? Jewish?
Y'all know this already, but just a reminder: preferences ain't beliefs. Downvote preferences disguised as beliefs. Beliefs that include the word "should" are are almost always imprecise: avoid them.
Additional rules: