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. :(