One alternative would be to attempt to select an analyzable structure which you could show through analysis should have good randomness properties. Potentially

One alternative would be to attempt to select an analyzable structure which you could show through analysis should have good randomness properties. Potentially add a limited number of tweaks or parameters with the aid of just one or two general statistical tests (and perhaps a collection of pants-on-head stupid tests just to avoid wasting time on stuff that is utterly broken). After that, you try with the complete suite and unless the result reaches a predetermined passing criteria you declare the design as flawed and go back to step 1 rather than continuing to tweak (as the result of continued tweaking will inevitably be a pass even if the design is poor). Unfortunately, high performance and even 'good random-like behavior' may be at odds with having a construct which is transparent enough to be able to justify its performance from analysis rather than running it. :(