I wouldn't worry about too much about whether or not you're completing a pull up so long as you're engaging all the muscles required to do the work in the program. I would experiment with adding the 50 pullups program as you described but pay attention to your effort level to check if you are over training. If there's a noticeable difference in the amount of effort it takes for you to do your modified pull up (ie harder time lowering yourself), then you are doing too much and I would advise giving your pull up muscles a chance to recuperate. As a side note, in my humble opinion, I enjoy simplicity so I would stick to one program until I feel a level of confidence or boredom and then move on to modifying it. But that's just me.
As far as pull ups go, if you are having problems with doing a full pull up, I would much rather try these two variations before your modified version:
1) partials (go half way down then up, count 2 of these as 1)
2) different grip
Lastly, I read one of your earlier posts and you mentioned your goal of going down in bodyfat. I think the simplefit program alone will help you achieve that, regardless of the type of pull up you do or whether or not you can do a "real" pull up so I wouldn't get hung up on it.
Currently dabbling in: IF, leangains, Starting Strength, 5/3/1