Also, instead of regular negatives, you could try frenchies:
Start with chin behind the bar, hold x seconds
Bar at eye level, hold x seconds
Elbows 90 degrees, hold x seconds
Bar right above head, hold x seconds
Dead hang (but still engage the muscles), hold x seconds
For reference, my climbing team held each position for 30 seconds and did it 3 times per work out.
This is basically a really slow negative, so it may give you more results than a straight negative. I'd like to cast another vote for the lat pulldown/assisted pull-ups if you have access to the gym. Also, you might start working out the individual muscles (back, biceps, shoulder) as well. Best of luck!