Lexus ES 2007-12 :: Strange Pulsing Noise And Sensation?

This is a lengthy explanation. Car has 135K on it currently. Had the transmission flushed and water pump replaced about 5K miles or so ago. The Lexus trio of lights came on about 2K miles later and I noticed a loss of power. It's like I'm cruising along and the sensation is that of a manual transmission car being in 5th gear at 20 and punching it; that lack of power that borders on the car dying but it never does. It just sputters along a little and then all is fine. No abrupt shifts, just like it's in too high of a gear and I've caught it off guard with my throttle request.

Had the codes checked, multiple misfires detected. Great, so I take it to the mechanic I use and they hooked it up to the computer and basically I need a tuneup, all the plugs and wires and boots need to be replaced. I don't know how many horsepower I was down but it was definitely noticeable and the idle would bounce between 750 and 1K RPM without fail. I couldn't leave it with them all day that day as I had a job a couple hours away and figured it had been fine up to then and it would be ok for four more hours. Wrong. About an hour into my trip, the check engine light, which was on, began blinking, which I was told by the mechanic is a bad sign and that something is seriously wrong. Power is way down, the engine is obviously suffering, it's rough and choppy, probably half power, couldn't go more than 30mph.

And it was accompanied by this pulsing noise in the rear of the car, beneath the rear seat If I had to guess a location. It wasn't a grinding noise, more whiney but not loud and it was in a constant rhythm. I pulled over immediately and tried to make arrangements for transportation. There wasn't a rental car place in the town I pulled over in, but there was a place the next town up. I get in the car and start it up and the trio of lights are still on but the check engine is not blinking and the pulsing is gone as is the car struggling to breathe. It's not great, but it's back to the way it was before and highway speeds are possible, etc. When I got back, I had the tune up and the catalytic converter and engine manifold gaskets replaced. It runs like a dream. My question is; what could make it run so terribly and cause that pulsing sound and vibration, that would somehow disappear by stopping and starting the car?