Look to using an electron gun to set the hydrogen in motion toward the plate where oxidation will occur.
You can find electron guns in old CRT monitors.
This will suffice for a cheap particle accelerator.
Peltier junctions for the system will be custom made, most likely from woven copper screening (like filter screen used in mining) and woven steel screening (same purpose in mining) in the 200 TPI range. This screening will be bonded to the plates. OR...One plate will be backed with steel, and the other backed with aluminum, or sandwich combinations.
Each time you use a different metal, you have a different electron shell, and each metal that has a different temperature will now give a differential potential in that electron shell. So with heat changes, you will garner electricity. If the heat is 600+ degrees on one side and -40 on the other side and you have a total stack distance of 6 inches, you have an EXTREME amount of electrical energy potential to be gathered.
Think............. outside............... the............... box............
AlaskaStar