Try a .01uf cap to ground or a .1uf cap to ground. The .1uf will be a LOT of high end loss if that's what you want.
For the LFO, try wiring up the LFO in the tremulus lune (just because I'm on a relaxation oscillator trip):

Basically the bottom two boxes. Then optocouple the LED to an LDR in series with the frequency potentiometer and you've got it. You can omit the fine pot if you want, and if you don't want the spacing knob just put a 470k resistor instead of the pot and the 220k resistor.
Good luck!
-Colin
I finally got around to trying Colin's suggestion. I built the Thing Mod on breadboard before, so I knew what it would sound like on its own. The LFO adds some very interesting sounds to the Thing Modulator. It can vary from wavering, to throbbing dance sounds, to twisted circus music and the guitar signal fighting the LFO.
Some quirks include being able to hear the carrier signal in bypass.
I tried the resistor and LED trick:
http://experimentalistsanonymous.com/board/index.php?topic=1809.0but I still hear the it.
The other strange thing is that when the LFO is going really fast the bypass LED blinks in opposition to the LFO LED. Strange since I wired it up true-bypass. It's weird, but also kind of cool/helpful.
Thanks for the tip Colin!