Thought of another way to connect a top half and a bottom half. Get some heavy dowling, maybe 3/4"+, drill into both the top and bottom sections (See my mods above) for a snug fit, then glue it into the top section. Put it in the center, and when you drill in for the launch rod, drill on into the dowel too, for extra length for that hole. An extra dowel could be used somewhere off center to prevent rotation, if desired.
Oooh! Better still. Instead of cutting the 4x4 into two blocks, just drill the 4x4 in the center for a 1"+ (depending on the launch rod diameter) dowel. Then drill the dowel for the launch rod, making the fit snug for the dowel and tight for the rod. Use different dowels for each rod diameter you want to support. You can glue (or otherwise fasten) the rod into the dowel, if desired. Optionally, a screw or long peg (possibly a thinner dowel) could be inserted horizontally to prevent the launch-rod holder/adapter dowel from rotating. If the holes are concentric, centered, and snug, there should be no reason to worry about twisting though. Just don't put any leg attachment holes through the central launch-rod holder hole.
Horizontal pegs or screws could also help in cases where the launch-rod tries to go up with the rocket. A Kaplow Klip arrangement or a screw and washer, as in motor retention, could be used for dowel retention as well. If doing that. I'd recommend drilling a screw hole beside the dowel hole, then digging into the side of the larger hole to intersect the smaller one and gluing a captive nut in there (again, much like motor retention). This nut would be held in not only by glue but also by being wider than the hole in the wood above it. Then run a machine bolt down the thin hole into the nut. You could also glue a bolt into the hole, attaching a wing nut to the exposed end, but that would leave a permanent "spike" on the top that's bound to get ya some time.
Makes for a very versatile system that loses very little in simplicity or cost.
If tilting is desired, a two part block could still be used. Round the corners of the bottom of the top block on one pair of sides (Think North & South.) Attach plates (wood or metal) to two of the sides (Think East & West.) of the lower block, and attach the upper block to the same plates (using a single large bolt and wing nut), leaving a gap betwen the blocks so the upper one can rotate when the wing nut is loosened. The rounded corners help and allow the gap to be smaller.
Brainstorming designs is fun!