Your engine balancer may simply have not done the job properly and missed something. Did he say if he had to add or remove any significant amounts of weight? Weight changes should be very minor unless something is out of whack.

Very doubtful that bearing clearances contribute at all to the vibration problem. Race engines run looser clearances than stock engines. If your oil pressure is ok, then unlikely you have a bearing problem.

Usually it's not necessary to align bore the main caps on a 4-cyl unless there is an unusual problem, but then the block is probably no good either.

Variables introduced are heavier pistons, different cam, balanced driveline. I assume you changed the motor and transmission mounts? What about compression ratio and ignition timing? Increasing the bore size increases the compression ratio. The "torque" cam can also increase the cylinder pressures (effective compression ratio). Are you possibly getting detonation? Maybe you can experiment with some other (retarded) ignition settings and see if things smooth out.

Otherwise it sounds like the balancing will have to be double-checked when the engine is next out of the car.