Methods for altitude changes

Thanks. I've visited that site before; the author becomes very abstract at
times, but it is useful information.

Personally, as an engineer and generally 'theoretical' guy, I enjoy
the abstraction... but I understand what you're saying.

By pitch climbing do you mean with the yoke, or with trim adjustments?

Yoke. Changing pitch attitude almost always induces phugoid
oscillations, with the yoke, those oscillations are trivial (almost
subconscious) to damp. Trim provides no such mechanism (without
grabbing the yoke anyways), so its generally a bad idea to fly with
it.

For any pitch attitude change, the general rule of thumb is pitch,
power, trim off pressure as necessary, in that order.

If I have nose-down trim applied to go fast at my low altitude, it seems I
should be able to trim slightly upwards and change altitude easily, then trim
back for level flight at the new altitude. If I already have nose-up trim
applied, this may not work, and eventually I'll have to add power.

It sounds like you're trying to fight the simulated phugoid
oscillation by using trim to make very low amplitude adjustments...
This just increases the period of the oscillations, it in no way
prevents them from occurring.

Power is a good, 'side effect free' mechanism of doing fine trimming
of your aircraft's altitude. In fact, I know instructors who advocate
only ever using the power to make the final 'lock' onto a new cruise
altitude, no matter what.

For example, the mechanism you would use to level off from a cruise
climb would be as follows:

500 feet below target altitude, push the nose forward gently to bring
airspeed up to cruise airspeed. Once you've reached cruise airspeed,
go ahead and trim to hold the attitude, but allow your power surplus
to continue pulling you up the last hundred feet or so to your target
altitude, only backing off the power the moment you reach it.

The descend-to-altitude is the same procedure, only with reduced power
instead (set up the aircraft in cruise attitude before you hit your
target altitude at a reduced descent power setting, and allow the
aircraft to settle onto target altitude before increasing power back
to cruise power)

I can see the theoretical advantages to this approach, but I would be
lying if I said I used to religiously (I still don't keep that far
ahead of the aircraft).