How does an end notch in a ceiling beam affect deflection calculations

The reason that joists are sistered using the same height of wood is simply space; generally there's no extra room. If you've got nothing below and there's space then there's no reason you can't use a taller piece of wood. Things to keep in mind:

• Spanning as much distance as you can so you transfer the load as evenly across the original joist. If it's too short it's going to still bow, just in a different spot, and you'll add additional stress on the existing joist.
• Don't weaken the original joist by drilling holes or cutting
• You'll need to raise the joist into the correct position before you glue and nail, otherwise you'll just solidify it in a sagged position!
• Prepare the surface of the old joist properly for gluing if you want it to take

400 lbs is not so large (consider that 2 or 3 people standing close to each other could easily exceed that), but you must be careful not to mount the hammock in a way that compromises the joists. Since the hammock supports pull at a diagonal and not straight down, the force exerted at each contact point is actually much more than the weight of the occupants.

It would be best to mount the hammock in the direction of the joists, so that one end is near the outer wall and one end is near the main center beam. The bending load on the joist will be far less than if you mount at the midpoint. Plus, the load from the hammock will be mostly in the axial direction, which is not a big deal.

If you must mount the hammock perpendicular to the joists, suspended from their midpoint, it would be best if the hammock attach point were at the location of cross bracing between the joists, and/or blocking if you have that instead. The bracing prevents the joists from twisting or shifting laterally, which otherwise would be a weakness. If you have no bracing between joists or they're not in a convenient spot, I would add some at the suspension points——say, 2 joists in each direction. If you mount the hammock this way, you must ensure that the joist do not twist or get deflected laterally, as that will severely compromise their stability.

As for attaching to a joist, I would not drill a large hole through the joists if you can avoid it, although it would probably be OK. Try to find a metal bracket at a construction supply store that will fit on the 2x8s and provide a support for your hammock chain. E.g. Home Depot carries several Simpson Strong-Tie products that look promising.

(If this is sounding like too much work or too risky, you could always pick up a free-standing hammock stand.)