I'd try different cables. I bought three 6' 24AWG High Speed HDMI cables from monoprice.com (for like $15 shipped) and use them between the PS3, the 3D converter, and the TV (Mits 73C10; electrically same as a 73638), and everything works for me. Now, when the PS3 switches modes, I get a "No Signal" or "Invalid Format" in the upper left corner, but it's transient (lasts a second maybe) then it clicks into the proper display mode. But I've been able to do 1080p gaming and BD, and had no issues with 3D frame-packed 720p@60 games, and 3D frame-packed 1080p@24 BD.
For less than $15, you can try quality cables and see if your problems persists. If so, there could be a different problem? But since I've (essentially) the same TV and use a PS3 (fat, not slim), I know the cables from monoprice work great for me.
PS: I've had the "no audio" thing happen one time when using the PS3, and wasn't sure if it was because I enabled 3D mode on the TV at the same time that the PS3 was changing display modes?