Dropping the lights to 4" WITH VHO's is prolly not that big an issue so long as you cut the photoperiod as well. Just gradually over a few weeks come back to your full photoperiod. There will not be much of a problem with this scenario, although if you DO notice any bleaching, cut the photoperiod in half and raise the lights as before, then start the slow acclimitization for the lighting over again.
Remember that the specimens you have now are going through a response to colony trauma: they've been cut off from a good bit of their normal shared nutrition (the encrusted base); they've been literally traumatized by handling, cutting/fragging, bagging and transport; they have new lighting and water in a new system; and they must now direct a good portion of their biosynthetic energy to forming a new encrusted base while attempting to still maintain normal biological processes of photosynthesis, translocation, calcification, and nutrient and gas exchange, most of which require energy expenditure on the part of the coral holobiont. Darwinian selection has chosen those individuals over the eons that are most successful at dealing with surviving trauma and still mainaining viability, so for the most part the specimens that historically cut unnecessary functions to survive are the ones we see today. This usually means that upward growth and coloration may not be the functions that enhance the recovery from these types of trauma, rather increases in zooxanthellae populations and density of those populations to provide synthetates to the host while it is expending the energy for repairs and processes that enhance the recovery (e.g., "browning" of the specimen).
You should expect this to occur in most frags for up to 12 weeks, depending on the size of the frag, its placement positioning, and the tank parameters in the new system. Remember that vertical placement of the specimen exposes the least amount of surface area to PAR, you would be better off to place your new frags horizontally, with the bottom of the specimen suspended over open water with a reflective white substrate... Not only would this give your new frag more exposure to photosynthetically active radiation, but by having more of the radial corallites exposed to PAR, you stimulate more of them to convert to axial corallites, increasing the eventual number of branches that branching or corymbose morphologies will develop.
HTH