More likely the retrofit would cost more than ten times the value of your
car    ;)

Engineers have been designing different doors since the first doors
were added to cars. Doors disappearing into the body work are not new
(for an example, see
http://www.conceptcarz.com/vehicle/z1723/Kaiser_Darrin.aspx ).

For this particular arrangement, imagine how thick the door is and
where it has to "disappear too." Then imagine what happens if you park
were there is some sort of minor obstruction under the car. To provide
clearance to make sure you can open the door (by sliding it under the
seats), you'll have to make sure there is always adequate clearance
under the car. Likely this means some sort of "double bottom." A floor
under the seats, plus a floor under the door storage compartment. This
effectively raises the height of the seating position by more than the
thickness of the door (probably more than 6 inches). You also need a
shape ("style") conducive to "rolling" the door under the car. And I'd
like to see the design for a four door version - maybe the whole side
rolls under the car at once. I am sure that will make for a strong
chassis. I won't say it can't be done, but I do think the compromises
involved are not worth the "coolness" of the feature. I can only
imagine the potential for misalignment, contamination of the
mechanism, rattling, etc., etc., etc. And how are you going to tie in
the guard door beams?

There are very good reason conventional hinged doors have been used on
automobiles for over 100 years. They work.

Ed