I am not aware if there is any such service provider. But its a great idea. If you can have a handy list of the domains available, I think you could strike much better domains. Any techie entrepreneur listening to this...
It's pretty much trial and error. If you're interested in finding out about all the LLLL.com, you could simply use a bulk whois checker to find out what is free - eg: https://www.moniker.com/login/login..../batch_reg.jsp
(you'd need a Moniker account to use this).