I used a similar idea to turn a couple dozen spindles for the sides of a
cradle, probably better described as tapered dowels.
I actually had a lathe as one function of my Shopsmith, but lacked the
skills to create uniform spindles. (and had no time to practice - baby
was coming soon!)
I made a small table that slid on the rails to support the router over
the workpiece. I offset the outboard lathe center so that it was
sufficiently higher than the drive end to get the needed taper, much the
same way the video jig has different height holes. The fact that I had
an actual lathe to rotate the workpiece helped. I had both hands free to
operate the router and because it spun the workpiece much faster than a
hand crank, no sanding was needed.It's been twenty years or so, but I
seem to recall several failed attempts while getting the adjustments
just right. Practice on something cheap before committing to your good wood.
The spindles were tapered throughout and glued into holes matched to
their diameter at either end. Table legs will probably need to retain a
square section at the top, I think it would be simplest to shape the
square-round transition with hand tools.