Has anyone ever successfully converted a recumbent bicycle or tricycle to hand-powered? How? What are the major obstacles to overcome?
Do you want this as an able-bodied person to play with, or as a disabled person because your legs don't work? If the latter, (two wheeled) bicycles are out of the question unless you're young, fit, and slightly insane (I say this because it's certain you will fall off a two-wheeler, probably more than once, and if the guy I watched/helped is any guide, you are likely to also fall off at speed at least once).
The problems differ based on the type of bike or trike. The most suitable IMO for conversion are SWB ASS bikes (short wheelbase, above seat steering) and trikes. The "hand-pedal" part is the same in all cases. Look at any handcycle, but essentially you mount standard handgrips on bicycle pedal axles, then add brake and gear levers. The cables from those need to be long as they flex as you pedal. The pedals mount to standard bicycle chainring(s) and a standard "bottom bracket" (even though it's not at the bottom any more). That bottom bracket mounts to the top of the steerer tube and the chain runs to a standard bicycle rear wheel.
The trike will be easier to ride and harder to fall off, especially up hills. Handcycles go up hills very slowly. Most handcycles for wheelchair users are trikes, normally delta trikes (often with with negative trail). Negative trail makes them easy to build, hard to ride, and unstable at speed. But since you're already looking at a few thousand dollars, easy to build helps to keep the cost down. The more expensive ones are usually better designed for speed (however I have been very unimpressed with the ones I've seen from a rideability point of view). The conversion can be very easy - you "just" build an arm with a wheel at one end, pedals at the other, and a steering pivot in the middle. You can even buy those premade as wheelchair accessories (http://www.riomobility.com/en/manualhandcycle/index.htm). If you can do that, scratch building the seat/rear wheels shouldn't be too hard. "Conversion" now means "chopping up random bikes to get bits" rather than "add hand-pedals".
But very few foot-pedal trikes are delta trikes, and the ones that are are slow. That's because deltas are inherently unstable, especially when braking and turning (very common in racing or in an emergency). A second hand recumbent tadpole is also likely to be easier to find. Search for "recumbent trike" and you will find a lot of tadpoles, few deltas. Converting a tadpole you'll need to insert a bicycle headset into the frame in front of the seat/behind the cross-member, extend that up, then build your pedal/steering unit on top. The chain will twist when you steer, but that's ok (world record setting speedbikes commonly do this). The chain goes to the rear wheel, and you'll need two idler cogs to bend it up to your cranks. http://www.TriSled.com.au in Australia have built at least one of these but it was very expensive (take a $4000 trike, add a couple of weeks work to convert it to a handcycle). It did, however, work very well :)
Converting a SWB bike is likewise fairly easy. Remove the existing stem and handlebars, build your hand-pedal setup to plug into/onto the existing steerer tube, weld on a couple of idler cogs, and you're done. Don't paint it yet! First try riding it. You will fall off, and may decide to revise how the chain idlers work. The first mount you build may well not be strong enough, especially.
In both cases you will probably find that having the pedal unit pivot forward makes getting on and off much easier.
One other option is a rowing bike - Thys make them commercially, and apparently they're not bad to ride (but they definitely work your legs as well as your arms)