I wouldn't divide the grasses now, unless it's an emergency situation. Better to wait and do it next spring, when it first starts to put on growth.

A couple of things about your ID of the grass:

The banding on the blades sounds right for Miscanthus sinensis 'Strictus' (Porcupine Grass), but the blooms should be reddish-brown, and this is amazingly early for it to bloom. Normally, August-September is it's bloom period. Do you recall when it started growing in the Spring?

Unfortunately I don't really recall when it started growing - I trimmed it to 6" high probably around the end of January, and I'm thinking that I noticed the first couple of new shoots around March - April timeframe. I do know that last year's height was a max of 4', and it had 6 - 8" long plumes at the tips that mostly survived through the winter - meaning some of the plumes were mostly there.

I think I figured out the flower conundrum, though - apparently when the previous owner planted this clump of Miscantus, he planted it in close proximity to some Spiderwort - which now looks like one plant after the past couple years.

Yea, I figured it was better to leave it be until next year, but it usually doesn't hurt to double-check. I can live with it, but it could be painful at times (the guy planted this right next to the filter basket on my pond - the filter basket that needs to be cleaned every couple of weeks or so).

Thanks again!