It isn't as dire or difficult as some of these posts make it sound.
No, a jackshaft opener won't work on a door with no jackshaft.
However, you can mount a standard GDO to the bottom of the floor joists, just not right above the door.
Open the door all the way, and mark where the top/back of the door ends up on the ceiling (at or between which joists).
Then mount your GDO to the bottom of the joists (as tight up against them as it can go), with the door end of the track just behind where the door comes to.
Mount the bracket to the top of the door as usual.
With the door in the down position, measure the distance between the bracket on the door, and a point about 6" back from the front (door) end of the GDO track.
Take a length of 3/4" EMT conduit, and cut it to that length.
Drill a 1/4" hole through both sides of the EMT about 1/2" from each end.
Cut a slot down the center of each end of the EMT, that extends about 1-1/2" in from the ends.
Use a 1/4" hitch pin or bolt with nyloc nut to attach one end of the EMT to the door GDO bracket and one end to the GDO traveling mount.
The GDO will pull/push the EMT, which will pull/push the door.