I might be missing something, but here is my thinking... the radiation coming out of the sun would always be perpendicular to your direction of travel around the sun at any given moment, so it would only ever be able to add delta-V and increase your orbit, not reduce it.

Unfortunately you can't do upwind sailing in a vacuum.

That being said, you can still use it for the method described in parent post, but you'd still need a different propulsion method to slow you down at the apogee.

You should be able to tilt your mirror/sail at 45°, so that the reflected light heads off in the direction of your travel, so that the momentum it imparts works against your current velocity, slowing you down, and degrading your orbit. Right?

Sailors have figured this out centuries ago to travel against the wind (called tacking). Some of the same principles apply, like orienting the sail so that photons push against the sail reducing the angular momentum.

Tacking works because you have resistance against two media (air and water) which are travelling at different velocities -- you need a keel in the water. Solar sails don't have an analogous second medium.

But they do! The (sort of) analogous second medium is gravity. You can “sail upwind” with a solar sail by angling it to reduce your orbital velocity.

"Sailing upwind" here -- if you were genuinely tacking, rather than doing something analogous to tacking -- would (with a big enough solar sail) let you propel yourself into the sun more quickly than gravity alone would pull you in.

So yes, you can produce a sideways component and let gravity do the rest, but that component can never actually push you towards the sun.

Sure, the analogy is loose, but as a sailor myself, I think it fits the fundamental ethos- one works the natural forces against each other to get where they are trying to go- wind, tides, and both aerodynamic and hydrodynamic lift.

The fact that one has a number of force vectors in varying directions with both sailing and solar sailing, both let you work them together in unison get where you want to go.

Quite often when I am "sailing" the wind is light or dies, and I go to "windward" by timing the currents, and wind at best lets me position for the right currents, but below a sufficient level produces no lift to windward.

Fair, although I think the analogy breaks down quickly enough that it's not necessarily helpful.

They can be used to decrease orbit as well. Since you just need to bleed off the speed from Earth's orbit, you could angle the sail diagonally so the the reflected light is pushing against your direction of orbit (sort of like how the fins on a pinwheel are angled).

While I was googling, a couple places likened it to tacking into the wind, but that's a different kind of phenomenon that works because of friction and pressure differences.

I think that if you're constantly being thrusted radially out, you don't actually gain delta-v or increase your orbit - you just shift it. Your apoapsis increases, but your periapsis decreases.

(It's been awhile since I've played KSP, I could be wrong.)

They can eventually decrease orbit toward the sun. They just need to be angled in such a way that the thrust is retrograde (not the sail itself). It would be incredibly slow though.