I would add that having a long-term strategy should not be incompatible with 2-week release periods unless you are releasing something brand new each time. So this depends on a scope of each release. Release scope defines the scope of testing as well: usually it is quite a challenging task to test absolutely everything for short release periods. Of course the bigger the better, but some priorities must be established.
Sure, automated testing tools seem to be the best way to deal with the lack of time here - given that you have such a solution which is compatible with CI and at the same time can perform regression testing properly. By the way, if you need to run some UI regression tests, I would suggest you trying Screenster, a visual testing tool which was designed to help with UI testing in CI environment.