Any ideas on the best way to mummify my Tube?

Forget the sonotube and use a piece of 4" white plastic drain pipe. You
can probably find a free 4' scrap piece at a construction site like I did
for my water shut-off valve.

If you want to insulate inside the pipe once its in the ground..take one leg
of a pair of panty hose and stuff it with insulation and shove it into the
pipe..