I've never been very good at pullups - I carry too much weight below the waist.
Don't be afraid to use the pullup machine - probably not a bad idea since you're coming off surgery.
Most of my back work over the years has centered around lots of rows and heavy rack pulls. It's not unusual for me to do at least 10-12 total sets of rows in a back workout - usually at least 4-5 sets of barbell bent rows, 3-4 sets of old school t-bar rows, and several sets of either seated machine low rows or one arm DB rows.
I rarely do more than 3-4 sets of pullups in a workout, and I can barely use much more than body weight for very many proper reps. But back has become my best upper body bodypart over the years.