I suggest having all your money in one account, but being able to "lock" a certain portion of it for a certain length of time (i.e. unable to use without a fee). The interest rate you get is proportional to the amount you have "locked". This way banks get their cash to play with, and I get my interest.
Obviously, this would only really work well with online accounts where it's easy to log in an "lock" your money. The bank site could have a bar chart showing each portion that is locked, what date it is locked to, and the interest rate it is getting.