If T bar's don't feel right to you than don't do them. My owned personal view, so take if for what's it's worth, but I would do rack DL's as the last exercise in the program. I know it's a cardinal rule to do DL's first, but that's not always the case for muscle building. I would also add another movement and maybe let go of the DB row.
I would suggest:
Pullover-bent arm, BB or DB..outstanding all around lat builder when done right.
Chins...medium grip... touching upper chest to bar each rep..change grips from time to time, including curl grips. If chins are not your forte than switch to lat machines, but touch the bar to upper chest...important.
Row...wider grip ..pull to the lower chest..elbows held out..hit's rear delts well also
DL...rack...Your back can take a lot of punishment, but why give it a lot of punishment... not needed. Give a fair opportunity for recovery & growth.
Might try 2 sets, 8-12 reps each exercise. If not happy, than try 3 sets a exercise and see what happens. Good rule of thumb is to start with the lowest amount of sets, at first, on a new program. Good Luck.
