I'll agree to fast healing for these.
Recharging other sheens: In the original text, it sounds like they also augment the rapid repair of the other sheens by using one of their arms. So if they repair the other sheens, they should lose one slam attack per sheen for that round.
Let's add to solar powered a little:
Solar Powered (Ex): A power tree gains power by absorbing sunlight. For every hour of exposure to natural sunlight (not a daylight spell or similar magical facimile), a power tree recharges x points of maximum damage for its defensive field and one daily use of its electrical discharge ability. If a power tree sheen is not exposed to natural sunlight for X days, it becomes inert.