hi and welcome to the forums.
firstly, I would say it sounds like you are doing all the right things in being supportive of your partner to get professional help.
the second thing I would like to mention is that he might be putting himself second to ensure you both have the things you need or want. There is certainty is doing a job you might hate - a bit like a pair of old slippers which are no good any more but you know how they feel. While the logical thing might be to find another job, there is the too much discomfort going down that path.
now I would probably agree with you on the talk therapy - at least that is what my psychiatrist calls it... medication and talk therapy go hand in hand. And despite your best efforts he does not sound "ready" to want to do it... at least yet. There is no weakness is getting help.
If there were a way to persuade him it would be to talk to him about the effect all this is having on you and speaking in terms of "I" and not "You" - it can help to lower the defenses of the other person..
sleep wise... if your partner is open to the ideas of "sleep hygiene" that should help with the sleep problems which can make the other issues worse. Things like getting 8 hours of sleep, relaxation before sleep rather than ruminating on problems etc.
I am speaking from experience here.
lastly there are pages on the beyond blue web site for supporting someone with depression. It took a year for my dad to get help with gentle nudging each week. You will probably sound like a broken record but ask him how he, and one day I hope you see a change.
Tim