I agree with Gary. Maybe you mean: “Although his career is solid, he has been going through a tough patch” or “going through a tough time.” This means that, for a short period of time, his life has been difficult, but things will probably get better.

"Living a good moment" is a bit of a cliché, I am a bit surprised that Gary and John didn't recognise it. I suspect that it may be found in styles of writing that they don't admire much - popular journalism, sports writing etc. They were capable of understanding it and suggesting good alternatives, but these might not suit the context as well as the original.

No, sorry, the second half is not very clear. Can you rephrase what you are trying to say? 'Moment' refers to a very short time, but 'living' suggests a long timescale.