It looks like it is even weirder.

Proper relativistic velocity arithmetics you mention is about special relativity theory - i.e. local flat-space case. Hubble runaway speed is supposed to be about global ongoing space distortion, i.e. it is strictly about general relativity. As far as I know, it is actually measured based on impulse change in photons, but it can be theoretically defined using time needed for a lightspeed round-trip.

When this relative speed is small, everything is fine; if I understand correctly, if Hubble constant is constant in the long term and there are large enough distances in the universe, it would take ray of light exponential time (not linear) to cross distances above some threshold.

In the inflationary model of early universe, there is some strange phase where distances grow faster than light could cover them - it is possible as it is not motion of matter in space, but change of the stucture of space. http://en.wikipedia.org/wiki/Inflationary_model