I had some similar problems driving two TVs from a TiVo HD through a HDMI splitter. Not as bad as yours (in that mine basically worked) but certain situations would lead to sound drop outs. I'm pretty sure this is due to HDCP handshaking. My TiVo was also driving the local TV on the component output.
What I wound up doing was:
1) Getting a powered component splitter (as just passively splitting the component didn't work).
2) Running the component through a component-to-HDMI adapter (also powered).
3) Running the HDMI adapter output to the HDMI splitter.
This gave me an HDMI signal without the HDCP. Solved all my issues. Monoprice has the component-to-HDMI for about $50. I found a powered component splitter for around $65.
Good luck with your issues.
What I wound up doing was:
1) Getting a powered component splitter (as just passively splitting the component didn't work).
2) Running the component through a component-to-HDMI adapter (also powered).
3) Running the HDMI adapter output to the HDMI splitter.
This gave me an HDMI signal without the HDCP. Solved all my issues. Monoprice has the component-to-HDMI for about $50. I found a powered component splitter for around $65.
Good luck with your issues.