Please define "floppy." Do you mean the new culms are bent over in a curve? Or do you mean that they grow out from the base at, say, a 45 degree angle? The latter is characteristic of young plants in some species.

The new shoots are tough & straight. Once they get some height on them, the FLOPPINESS occurs.

Remove the top. The excess weight is the problem because the top is not strong enough.

Tie a rope around the grove. Flopping to the left will pull on flopping to the right and help hold the whole grove more upright

Otherwise if they are soft and watery cut them off.

my new Ph henon and nigra culms were arched over the ground when they got about 4 or 5 feet tall, as the new branhces and leaves arrived. I tied them up to adjacent culms, and now all are upright, but I think they would have straightened up without the tying. Same with a couple of my Queen palms.

New fronds/leaflets arching over to the ground, but stiffen up eventually.

I have the same thing going on with my yellow groove. Its their 2nd year now. I've fed and watered all summer, and the plants got so heavy (leafed out very well!) that they droop big time! The boo lays down in the rain! Should I care? The wind really makes the entire little grove swing all around, but I have not lost any culms to the movement yet.

In an unrelated boo question... Should I cover the rhizomes at the base of the plant? They look like culms that plunge downward and disappear. Should I mulch that area heavily? Is that the normal pattern?

Ian-
1) When I have culms that bend way over (particularly in the rain) and get in the way, I tie them up to one another or to a central bamboo stake using either transparent fishing line or green twine.
2) Your rhizomes are acting normally. Cover them or not...it makes no difference. However, mulch is always a good idea in general.

Hmmm, my Yellow Groove has been a bit floppy too, more so in the last month or so when the rhizomes have been expanding like the dickens. Coincidence?

I think I'm going to add some Viagra to my automatic watering system, should get them straight in no time. :-o