Chain mouth bits can work just fine...on a horse that likes that much motion in their mouth with a rider that knows how to ride in a chain mouth.
Unfortunately, bits like that are sold to every jane, sue, and molly that want one, regardless of whether they know how to use them or not.
Chain bits are about like twisted bit; they have their place, but in the wrong hands or on the wrong horse, they can not only inflict pain, but do actual damage
Also, that first hack combo that you posted is awfully powerful when you're just stepping up from a french link snaffle. It's got some really long shanks on it and some pretty massive gag action.
If I were looking to upgrade my horse from a french link snaffle into a combo bit of some kind, I'd likely start with something like this... DUTTON BITS - Dutton Dogbone Gag w/ Rope Nose Bit - NRSworld.com Ring Combination Rope Nose Hackamore - Reinsman
Neither one of them is something that I would really want to use on any of my horses, but they are about the mildest versions of a snaffle/hack combo I could find.
Have you thought about maybe trying a full cheek snaffle with the same mouth you're using now? That will give you a bit more lateral control without upping the power.