In this context, I would just manually draw a shape layer (or large solid with masks) to match the shape of the reveal. Match that up with your animated square and parent it. Use this as your matte layer - it'll be super-fast compared to using Echo.
Your video shows a yellow square, which I assume is over the logo moving in a zigzag path from the top left corner to about the bottom middle of the frame, then to the top right then down. There is a wipe that follows first the top right and bottom left corner then the and bottom right corner of the yellow square making kind of an offset W shaped transition.
I don't see anything at all in the sample video that looks like the echo effect.
Does the video represent what you want to see or what you are seeing? If you want to use Echo, it is going to take a while to render and 15 minutes to render an 11-second video isn't bad for a lot of effects. You could cut the render time down if you started the comp with the shot of the motorcycle at 3 seconds and just made a match cut in your NLE. I routinely do composite and VFX shots that take more than a minute a frame to render on a very powerful desktop machine so 15 minutes a frame for an 11-second effects shot could be very acceptable, but as Kyle said, this transition could easily be accomplished with an animated layer for the logo and an animated mask with only about 6 keyframes as a track matte for the underlying video.
If you really want to create some kind of echo transition, let us know and maybe we can help.