woo a topic I can be useful on!
Mike! I have bent a lot of wood. Thin lams are probably the easiest/fastest way to go. The downside of that idea is you need to make it wider than 3" because the bits slip a little and whatnot and the glueline can wonder on you if you don't have clamps everywhere, like every 2". Then you have this wider than 3" piece you need to trim up flush and whatnot and that is kinda akward.
If you bend the whole thing at once, 3" is a wide piece and there won't be much finesse to it. A piece of stovepipe and some aluminum foil over a stove or a campstove and a pot and you have a steamer. You steam it for a long time and they are right you want an hour or so for a big thick piece like that then you want to pull it out and stick it on a form real quick but it is wet and heated by steam so this is hard to do. One end of the form you want a block on the outside to trap the piece so you can just stick it in and start bending. It is helpful to have a backstrap along the outside of the wood like some metal strapping or something to keep from raising splinters and it is clamped at both ends of the piece you are bending. The heat from the steam does start to dissipate real quick but you can supplement it with a heatgun and get results that way. I kinda think you would again want a piece slightly wider than your target width because the sides will mush a bit.
Pick a real straight grained board it won't splinter on you as easily. If you can use white oak and cheat it is known for bending very easy with heat/steam. I don't mean to offend by giving the dictionary but there are a lot of hints/tips to bending wood, kinda food for thought.