They grow fine from "Root Division" and of course seed. We grow all ours from seed and now found a hybird of yellow flowers on some that we've marked for future collection. Once these are established (and it sounds like yours is) it will come back, if its large enough you might consider digging it up and dividing it into sections then re-planting each section.

My [false] Red Yuccas are well established, and have increased the number of spike shoots. However, on some of the plants this year, the spikes, which are usually mostly upright, are laying over, Some are about horizontal, some touching the ground. Does this just happen on occasion, or is it an indication of something wrong?

I have some that have been run over by cars, cut with mowers, and just about anything that could happen and they have all come back. As a matter of fact a number of my abused red yucca are pushing flower stalks as I type this.