So you don't want a whip, as it makes the Smart Car look like a "RC Toy" (although some in the hobby, me at least, will disagree, afterall antennas on cars are fantastic)
And you don't want to hinder and doors/trunk/whatever opening, as you use the vehicle for certain purposes... (fair enough)
And you cannot use any mag-mount, as the vehicle is largely plastic, which also means you don't have a "ground plane" or whatever name you want to give it. (Technically the metal horizontal parts of a vehicle will act as a capacitor to earth when properly bonded. But some think the car itself is the ground plane)
You are thinking of a "slot antenna" but just to realize that a "slot" in the "slot antenna" is the same size as a 1/2 wave dipole, the "slot antenna", besides that it will be directional (not good for mobile use) will be quite large... which you do not want (the "RC toy" effect again)... as well as difficult to mount. If you have already a problem with 1/2 wave whip, then the slot will be even bigger.
Furthermore, it will be doubtful if you can actually use a slot antenna for VHF, as these are mostly designed for much higher frequencies.
If you don't mind doing a bit of DIY: you can get antenna's for the 87-108 MHz which you can stick to a windscreen (front or back), example:
You will have take out any active/passive components, and tune it for 2m. But it will not obstruct doors, it will not have a visual impact.
Efficiency and how this works is hard to say. I have not done this (yet).
To answer your specific questions:
Would a Slot antenna cut into a piece of 1.5 inch wide, 1/8 inch thick
bar stock work? Minimal expense and I can get it almost anywhere.
That is not how a slot antenna works, please look up some designs online. Examples:
You will quickly find that your approach is too simplistic to produce a working model.
Would that be better than just cutting the slot into the bars? I can't
find out if that's very directional, I assume I'd cut it in the top
and use weep holes, cheapest option.
As per previous answer, the design is much more complex. (and) Yes, a slot antenna is a directional antenna which is not suitable for mobile use.