I've looked at this issue as well, mostly in Firefox. I wasn't aware it would work in Chrome; that might be a recent change. Short of FF changing to recognize bookmarklets as being outside the policy (as it should!), there is no work around. The script won't run, full stop, you are dead in the water.
Alternatives:
1.) Create an addon; or utilize an existing addon like Greasemonkey to run a userscript.
2.) Run the code in the web console. In FF, CTRL+Shift+K gets you there in a jiffy.
3.) FF's developer scratch pad also works. If you save the code in a file, you can access it relatively quickly using Shift+F4 (open scratchpad) > File > Open Recent > select your file > CTRL+R (run).