Hi @odinserj,
I apologize for very late reply on this one, I have no idea how I have missed your reply. I got back to forum after googling something and noticed missed notification 
You told “caused that connection to Redis was opened after several attempts, when TaskScheduler actually got a chance to run the connection-establishing task”, and if you are sure with this statement, I can try once again.
Well, judging by log entries (several unsuccessfull and then successful), after some time hangfire did connect and started processing tasks.
So yes, I could say that I’m sure that the internal default task scheduler was getting overflowed and couldn’t keep up with the amount of work I gave to it, causing issues with Hangfire as well.
Have a good one! Cheers!