Plenty of publications reference the idea (such as this snippet from Popular Science), but did anyone take it seriously? What did astronomers of the day (other than Shklovsky) think of the idea?
They took it seriously enough to publish a rebuttal to it 3 years later, as is documented in Wikipedia. As is well known today, there was an error in the mathematics. Specifically, Wikipedia quotes:
Singer's critique was justified when earlier studies were discovered to have used an overestimated value of 5 cm/yr for the rate of altitude loss, which was later revised to 1.8 cm/yr.
Bottom line is, it was taken quite seriously, but it was discounted rather quickly afterwards.