Fkrst of all, Im no master mechanic. BUT Damn man. I hoped you'd figured this out.
You've gotta have air trapped or air getting in. Given the fact it kind of drives immediately after bleeding it sounds like it is letting air in. Did your new hydraulic line come with new o-rings?
How sure are you that the master is new?
Could very well be that the slave is compromised. If I was in your shoes and planned to keep the vehicle long term, I'd be replacing all of the hydraulic components that I didn't purchase and install myself. If you're going to go that far it'd be a damn shame not to just replace everything on the way in. It's the more expensive route, many would say it's a waste and it's overkill. Right or wrong though, it's what I did and would do in your shoes. If it's at all possible for you that'd be the route I'd go. If you have an extra set of hands just for the transmission removal and install the jobs really not bad.
If you're confident in the master, you already installed the new line (and o-rings) and you have bled the hell out of it then the slave sounds like the culprit.
Good luck bro.