How does one scale encryption strength upwards from 256-bit?
As @David Schwartz said, using something like 3AES should work to scale up the security (but see my comment on the meet-in-the-middle attack). But seriously, why would you even need 512-bits of security in a symmetric algorithm? According to the analysis on wikipedia it would take 50,955,671,114,250,100,000,000,000,000,000,000,000,000,000,000,000,000 years to bruteforce 256 bit AES (given a few assumptions on speed). I doubt you have any data that needs to be secured for that long.

As far as whether the CPU limits the security strength, it doesn't. There are libraries out there which provide "infinite" precision numbers (i.e., gmplib for c/c++, BigInteger and BigDecimal for Java, etc). For more on computing with large numbers, see chapter 14 of the Handbook of Applied Cryptography (HAC). Internally, these libraries use things like long long int or even plain int stored in an array. HAC has the algorithms.