A Henry J was converted to battery power back around 1970 by a father and son team (last name Templeton) in Illinois. The car was equipped with a fork lift truck electric motor with 6-volt type 1 case batteries in the engine compartment and trunk. The car had a top speed of 45 mph and a r ange of 65-90 miles before recharge (which was an overnight thing) depending on speed and terrain (hilly vs. flatlands). This car was sold by the Templetons only to find out that the buyer wanted the car for body and frame to make a hot rod; they also never got paid for the car. I got to see this at the first KFOCI National Convention (PA, 1975) both on the road and parked. No noise which always make me feel uncomfortable.
You need a platform that has a 115 inch wheelbase for the conversion if you're doing it off a 1951-55 Kaiser; consult factory specifications for wheelbases on other possibilities (Henry J, Frazer, etc). Remember you may be moving a total of 4,000 lbs or more with the electric system and that could cut into performance factors (speed, distance on a charge, etc). Emisions and safety equipment may be a problem is that some states might license the finished product based on the engine number (which would tie back to make and year the engine was built). I am not a mechanic or automotive design engineer so could not scope it out but it should be noted that Ford and GM had to start from scratch on the current projects rather than adapt an existing car platform to full electric capability. If this is not enough, figure that at between 100,000 miles to 150, 000 miles you would have to put in a new battery pack (mileage assumes you would have started out with a brand new pack) on the car. Unfortunately, these battery packs have a shelf life so even if driven less than 3,000 miles a year, the battery might poop out after 6-8 years.
I am not saying don't do it, but if you do, pick a donor car that would otherwise need major restoration especially on the first try in case the first try develops engineering/construction problems you can't work your way out of.
Regarding the company in Wales (part of Great Britain) that does conversions, I suggest you get a few "testimonials" from car owners to see if they would do the conversion again if they could do it over. You may be surprised at the answers!