This is an interesting idea. But presumably the person who initially made the tx on the main chain would have to be the one that signs the tx that another person can redeem on the main chain. But that person cannot then transfer it to someone else because his signature won't meet the main chain's script requirement. In this respect, no data is really saved anywhere. But I could very easily be missing something.
Well, I'll try again...
Suppose we have two separate chains: Bitcoin and Fastcoin. Bitcoin is more secure, but isn't friendly to microtransactions.
Suppose a market maker John notices that a unit of Fastcoin is more valuable than unit of Bitcoin, so he sees a profit opportunity in converting Bitcoins to Fastcoins and selling Fastcoins.
He creates SPLIT transaction with 100 Bitcoins he has. Now he gets 100 Fastcoins, and he can then sell (or spend) them...
Later he finds that Fastcoin drops in value: 1 Fastcoin = 0.95 Bitcoins. He now wants to convert Fastcoins back to Bitcoins.
To do that, he first buys Fastcoins on market. Then he creates DESTROY transaction on Fastcoin chain. And then he creates a MERGE transaction on Bitcoin blockchain.
MERGE transaction uses output of a previous SPLIT transaction, so on Bitcoin side it follows same conservation rules as a normal Bitcoin transaction. It is like sending 100 Bitcoins to yourself with additional condition.
MERGE transaction needs to reference DESTROY transaction.
Miners can check whether referenced DESTROY transaction was included into Fastcoin chain via SPV.
However, note that Bitcoin strictly follows its own conservation rules, so you have same guarantees as before. It does not mean that we are using SPV for Bitcoin.
What happens if there is a deep reorg on Fastcoin chain?
When miners include MERGE transaction into Bitcoin blockchain, they will stamp Fastcoin blockchain at the same time. Miners who mine subsequent blocks will have to take this into account, i.e. if there is a fork they should be stamped chain as valid. So there is never a disagreement about what Fastcoin chain is valid among Bitcoin miners.
This means that stamps-from-Bitcoin-chain can override Fastcoin's own PoW.
On surface it seems to make Fastcoin less secure, but as TierNolan have noted, a delay can make attack-via-Bitcoin infeasible.
I'm not 100% sure, but there might be a way to match PoW so that attack-from-Bitcoin costs no less than usual 51% attack.
So here's what we get in the end:
1. Bitcoin is exactly as secure as before if MERGE transaction can never produce Bitcoin blockchain forks or orphans.
2. Fastcoin is just as secure as a merged-mined chain.
3. Fastcoin can use UTXO-based security if necessary, however it might be just an offload.
4. Overhead in Bitcoin chain is minimal.