To work the bands, you need to emphasize speed. On a close grip bench, speed can be a dangerous thing, especially if you are already having shoulder soreness with the movement. Board pressing should not affect your ROM if you properly set up your routine.
If you board press with 3 boards from now until infinity, it may, but if you are really nervous, you can run smaller board pressing cycles followed by regular bench cycles and run low to high. such as (3 weeks 1 board, 3 weeks none)(3 weeks 2 boards, 3 weeks 3 none)(3 weeks 3 boards, 3 weeks flat)
If you are interested in using the bands on the close grip, i would set it up to be over 5 sets for 3 rep intervals. Increase the negative (3 secs.) and explode the positive (1 sec.) emphasize explosion on the positive and total control one the negative. Bring the bar deep into your chest, and focus all the energy of the positive through the triceps.
I say this because if you go too fast, you will start the movement with your delts, this would lead to more shoulder issues. Also, i would not use this as my main compound lift for the day. I would use it as assistance work solely to emphasize triceps strength. Dont get cocky and too much weight, if it a controllable weight feels too easy, decrease time between sets and work from more of a fatigued state.