Did you see my earlier post? Just make a false bed for your current planer, and you can go as thin as you want. Just take a piece of masonite, or melamine coated particleboard, plexiglass, anything smooth, etc. and clamp a strip to its bottom side to form a ledge that rests against the infeed side of your machine. I keep this jig by my planar and slide it on top of its bed whenever I need something thin.
You just have to experiment to see how thin you can go before the wood gets so thin that the force of the knives and the feed rollers actually rip it apart.
1/8" should be no problem. That is about how thin I would go for my application when I used the false planer bed. I was making bottoms for jewelry box drawers, and wanted to keep them a thin as possible to take away as little storage height as possible. I was working with straight grained american hardwoods, so tear out wasn't to much of an issue.
You can do this in 5 minutes with your current setup. If it doesn't work well, then look into the thickness sanders. I think they are down to the $500 range for the smaller cantilever designed woodworking models by the lower brands like Ryobi. I think the Performax models are still above the $1000 range, but a quick check online will give you the current prices.