If that is the goal, though, it would be better to use two well studied encryption methods rather than something homemade.
I would happily bet $10,000 that AES will not be broken in the next ten years. I'd make the same bet for several hash functions.
And as a corollary to this point: I think it's incredibly foolish to try and combat the threat of an encryption algorithm being broken by double encrypting a plaintext, including with that algorithm.
What are you talking about: http://cr.yp.to/antiforgery/cachetiming-20050414.pdf
You'd lose the bet so hard. Don't take anything for granted. Even the most supposedly secure and widely used primitives should be scrutinized and are subjects to constant attacks.
Read that paper again. Cache timing attacks (and more generally timing attacks) are a subset of side channel attacks, which are not a break in the fundamental design of a cryptographic algorithm. When Bernstein mentions that he considers it a design flaw, that's a misnomer in the mathematical sense: he means that AES is antagonistic to a software implementation that can resist a timing attack, not that the design of the algorithm is fundamentally unsound. This is essentially true for all encryption schemes that utilize lookup tables and S-boxes, which he even mentions in the paper.
This is similar to using acoustic analysis or fault injection for key retrieval - yes, you've done it, but it's not really fair to say you've broken AES whatsoever. That remains a pipe dream. You've merely broken an AES implementation on a particular platform that was not hardened for this threat. Just a few months ago a team came up with a way to retrieve an AES key through acoustic analysis in a paper that was published here on HN. That's not actually the same as a cryptanalysis, the best of which is this: https://eprint.iacr.org/2009/317
There are effective CPU mitigations that allow you to safely implement algorithms in order to avoid this issue - for example, AES-NI theoretically mitigates cache timing attacks. See: http://cseweb.ucsd.edu/~hovav/dist/aes_cache.pdf
So: no, I wouldn't "lose that bet so hard."
AES isn't proven to be secure. I don't know about $10k, but I would not bet my life on any hash function not being broken.
Also, please be nice.
Note, though, that you are using the specific word 'algorithm', where as I am talking about 'methods'. Most cryptographic failures are in how the algorithms are implemented or applied, not a problem in the underlying maths.
I would not be nearly so confident about a similar bet that applied to the actual code being widely used for encryption.