I find it very interesting that you can't keep them down. I've had anacharis in my 29
gal since I pulled ~1" shoots from my "growing tank" (supply house for my whiskey barrel pond). My goldfish hasn't pulled a single shoot out yet, and goldies are notorious for uprooting plants. I have about 12 plants (single shoots: some bunched, some not) ranging from 1" to 12".
I've found that if you bunch them, they'll stay in place better if you have a fairly strong current or fish that play with them. However, the single shoots seem to hold their own as well.
As for the roots, as mentioned, they don't traditionally root. You'll get these little tentacles that sprout off from the shoot (seems to be at new growth points). They will dive down to the substract and will take foot there. Not too appealing, but not ugly enough to keep trimmed. In my tank, it takes about 12-14 hours for a foot to go about 6".
For planting, I don't do anything special except put them straight into the gravel, all the way in. I have about 1.5" of gravel. I then mound it up a bit around the base, just to give an extra 1/2" or so. My goldfish eventually moves the mounds, but it takes him a while.
You may try NOT stripping the stems down. The extra leaves may provide a bit more of a foothold. I've never stripped anything down in the year or so I've been growing Anacharis and never had a problem with the leaves rotting or anything.
I'll take some pictures tonight when I get home to give you an idea of a structurally sound group of Anacharis and what to expect. This stuff is a weed I tell ya. It's pretty stable after a good 24 hours, and even more so when the spouts take foot.
