The method is based on Max's marvellous _FXGraph3D and uses parametric equations from the equally marvellous MathMod.

Copy (Ctr-c) the following and then within Moi hit Tab and paste (Ctr-v)

_FxGraph3D cos(v)+u*cos(v/2)*cos(v);sin(v)+u*cos(v/2)*sin(v);u*sin(v/2);-0.4;0.4;0;6.20;15;15;1;1;1;UV

Or, using Notepad++ save the following as MoebiusStripSolid.js (no spaces) and then copy MoebiusStripSolid.js to the Commands folder and it will show up as MoebiusStripSolid in Max's UI ext scripts feature.

moi.command.execCommand(' _FxGraph3D cos(v)+u*cos(v/2)*cos(v);sin(v)+u*cos(v/2)*sin(v);u*sin(v/2);-0.4;0.4;0;6.20;15;15;1;1;1;UV' );

Note. If you have done what I apparently have foolishly done and omitted the leading underscore of _FxGraph3D in your set up then you will need to omit it from the preceding lines.

The resultant mesh should be a Moebius Strip mesh with a bit of a gap in it. The gap is necessary for the time being and will be fixed later. In case you're wondering the gap is caused by using the value '6.20' instead of '2*pi'.

Select the entire mesh and execute Construct/Network using Mode:Normal
Delete (or hide) the mesh, select the surface and execute Construct/Offset/Shell using Thickness: 0.06 mm, and Direction: Centerline. This should result in a solid with a small gap in it.
In the gap, select and delete the two faces that are, well, facing each other. The result is a Joined srf.
Choose one of the new openings. Select all 4 sides then used Ctrl-c and Ctrl-v to copy and paste them. Use Edit/Join to get a Closed crv.
Repeat for the other new opening.
Select both new Closed crvs and execute Construct/Loft using options Loft Style:Straight and Profiles:Exact
Delete the two Closed crvs used for Loft.
Select everything and execute Edit/Join.
Result - a Solid.
Happiness and joy.