HDMI Mixer/Blender/Superimposer-Chip (2 to 1) wanted
I do NOT think there is a single chip solution neither. However doing this with an FPGA-based platform is certainly doable. As already mentioned the Digilent Atlys Board could be an alternative since you have there 2 in/ 2 out HDMI ports.

In case you consider working with FPGAs:

First, I would suggest to start with the design of a HDMI transmitter and receiver. There is another question that gives a good starting point. Then, the overlay can be achieved with an HDL- implementation of the alpha-blending algorithm which can be used for mixing 2 images into one. The good point is that this gives you the possibility to configure the level of transparency of individual picture elements.

In few words: being x and y the inputs and z the output video signal. An alpha-blender circuit can mix them implementing the equation:

z = x.(alpha) + y (1-alpha); where "alpha" is the coefficient or level of blending.

Finally, you can integrate the previous blocks making the following processing chain: HDMI receivers -> overlay logic -> HDMI transmitter.

I hope this helps!