I'm having the exact same problem as of a few days ago. My internet connection is ALSO not the best, and on top of that, I have to stick to a very strict data 'budget', so I literally CANNOT use the data heavy options of the Tumblr app, or Chrome.
I've basically always used Opera Mini for Tumblr, and once when I couldn't log in, I did find the solution of setting the single column view/mobile view to on, and it used to work. But now it now longer does. I tried logging in on Opera Mini on my Android a few days ago, and NOTHING worked.
I REALLY need a solution for this problem, as I use Tumblr more than any other 'social' platform, and I think I'd go a littlw nuts without it. There HAS to be a way to solve this, in this vastly technological era of ours?!