Leaving it down shouldn't be a problem, especially for the new growth. Personally I use aphogee 2-step protein treatment from Sally's once a month and I'm also using kinky curly stellar strands deep conditioner at least once a week. However, I would check the different forums and try to get an idea of your hair properties so you have a better idea of what might work for you. I've never tried the inversion method but 4 inches a week is extremely doubtful. I believe the average hair growth rate is 3/4 inch per month and your hair looks quite long so to completely grow it out would likely take at least one-two years.