I've been modifying my '63 544 bit by bit for the last few years. It started out as a bone stock car that sat for 15 years under a carport when the brakes failed. I apologize in advance for not having the good info you are looking for in regards to B16 engined 444 cars, but hope the info is somewhat useful anyhow.

B20 engine conversion: My '63 originally came with a B18 so fitting in a b20 is exceedingly easy. But I think the B16 engined -'62 cars are not -quite- as easy. The bottom radiator hose is on the wrong side, and some sort of pipe or long hose needs to be rigged. My own car has a B16 nose for some reason (old crash repair) and has a metal tube running across the front near the pulley - and uses two of the stock hoses on each end. In my experience the B16 radiator has a hard time keeping up with a somewhat perf built B20 engine (mine is 2.2 liters) so an upgrade recore might be needed if you don't want to have to use the ehater on warm days when driving 'spiritedly'. Motor mounts are another issue - you just use the mounts on the 544's B18 when fitting the B20 - but I don't know and doubt that the B16 mounts will work on a B20. An important issue to note is that the 544 mounts are straight up and down, while 122 mounts are slightly tilted backwards, and 140 mounts are tilted even more. Those tilted mounts are designed to balance against a forward tilted motor mount, and won't work well for long with the bushing tranny mount on a 544. You probably will need to get 544 B18 mounts from somewhere (unless you redo the tranny mount as well). I think the clutch linkage is a little bit different between a B16 and B18 installation too. Come to think of it you probably want to get an entire B18 544 drivetrain??? The carbs, the starter, the mounts, the bellhousing, clutch linkage, tranny, and driveshaft would all make fitting a B20 into your car much easier.

When you get a 'core' B20 you might as well rebuild it with some performance parts instead of rebuilding it as a 120 HP stock engine. With a cam, an overbore and bigger pistons, and a little head work 150 - 160 HP is easily achievable with some. And the lightweight 444/544 makes the most of it! >:^)

rear end: A B16 engined car will have a VERY low rear end - a 4.56:1. With more HP from a B20 the low gearing will be painfully obvious - while it would then have the power to hang with the traffic at freeway speeds the revs required would dissuade you quickly. While later B18 engined ones had 4.10:1 Dana 27 rear ends and can be regeared a bit more easier (Jeeps also used Dana 27 diffs and lots of ratios are available) I'm not sure what earlier B16 444's use.

transmission (maybe mustang or toyota?): Even with the 4.10 rear end in my car it was still painfully undergeared but instead of messing with it (and raising the ratio for all 4 gears) I put in an M41 OD tranny. Note the the tunnel in a 444/544 is VERY narrow, short, and cramped. I doubt you'll fit anything other than an M30/M40 without cutting out the original tunnel. I cut a shockingly huge hole in mine and replaced it with a 122 tunnel. I think some Australian outfit (Dellow???) makes bellhousing that mount Celica 5 speed trannies to B18/20 engines. As for driveshafts - if you have the ends and know the length machine shops that specialise in powertrains can whip you up something that will work. They do it all the time for hot rodders putting engine A into chassis B hooking up to rear end C. It only cost me $40 or so to have mine shortened 11 3/8 inches for my OD installation.

Suspension: www.KgTrimning.com has Bilsteins for 444/544's (only place in the world that I've found). They are also by far the best source for performance B18/20 parts as well. IPD sells swaybar kits which absolutely transform the handling of the car with no deteriation of ride comfort.