Good question. I don't recall if he got very deep into cosmology even after he realized Lemaitre was right, after initially calling Lemaitre's physics an "abomination" (

). There were a half-dozen or more that were very active in cosmology using GR, including De Sitter, Wrey, etc.

One problem was in determining any sort of an accurate value for the expansion rate, which would give those > c values. Lemaitre and Hubble had, initially, very fast Ho values (around 600 kps/Mpc, I think). Lemaitre had too little to work with and he knew it, which is why most people think he didn't bother to include his expansion rate in his English translation of his now famous 1927 paper that was the foundation for BBT. Hubble had, during this interval, since produced a lot more distance measurements that refined the expansion rate. Hubble also seems to have been quite jealous of his (don't forget Humason) work, so this human element may, or may not, have played into this story.

Hubble, initially, was not aware that there were two types of Cepheids and thus, two values for distance determinations. He greatly underestimated the distance to Andromeda as a result, which gave him a very high value for the expansion rate. This gave us an age for the universe deemed younger than the age of stars. [I can imagine the fun we would have had back then in any forum threads!

]

This error was corrected quickly, IIRC. Then much later came the SN Type 1a to greatly improve the expansion rate, as well as, the other techniques you've mentioned. A really solid number doesn't exist due to some conflicts but the probability seems very high that it's between 60 kps/Mpc and 75 kps/Mpc.

However, I can't imagine Einstein would have had any problem with spacetime expanding faster than c. The fixed value of c is always motion through space only.