HT,
One possible reason your chara came back more after raking is possibly due to the fact that by raking it out you also broke up the algae beds and allowed pieces to drift to new areas and re-establish in the raked areas. I know this can be true with true rooted plants, i'm not positive if this is also the case with chara, but it's possible. The bloom is probably due to the lack of nutrient uptake which was once done by the chara that was raked out. The nutrients are still in the water and will be utilized one way or the other. If you do use chemicals it is easier to treat chara in it's earlier stages before it's calcified "exoskeleton" forms. For chara you'll use an algacide and at approximately double the rate of filamentous algae. It'd also be advantageous to use tubing to get the spray underwater in close proximity to the chara for better contact before diffusion into the water column. If someone has used copper or cutrine granuals on chara I'd be interested to here how it worked. Chara will spread underwater pretty fast like most agae does. It acts as a good filter in your pond and you may notice some clearing of the water due to the chara mats, however that increased the depth that the light can reach which inturn may promote more growth. Good luck.
Mike