Clip off the two larger splinty branches and put the plant directly under the fluorescent (about 5 inches, monitor if you don't get burns or Black pigmentation spots). Peppers will set pods under fluorescent, though not as reliable as under direct sun light. I now have 7 pods under my 6500k grow light, with about 100 billion flowers dropped. So it should work better with coolwhite.
Also try to knock the humidity up a bit, but a bowl of water on your radiator or put a humidifier on. 50-65% gives a lot better pollination.