Hell in a Handbasket as a very good post up on some innovative firearms designs that ultimately failed to succeed. Go check it out here.
As I read a few thoughts occurred to me.
The LeMat- make it a break action like a Webley so that the revolver cylinder and shotgun can both be loaded at the same time. It would obviously require some ingenious work to re-fashion the design so that the shotgun barrel was firmly locked in place while the cylinder continued to revolve around it but I'm sure some engineering whizz could figure that out. These days I'm sure some would want to see the shotgun chambered for a .410 shotshell but personally I'd opt for a 20 gauge or 16 gauge.
The HDH Machinegun - this is a neat idea and a weapon that I'll admit I'd never heard of before. Seems to me that the time for another double barrelled revolver has come- it evidently needs a small cartridge so why not go for a rimmed version of the P90's 5.7mm or HK's 4.6mm?