Measuring any part of the wheel, rim or tire, is always going to be a challenge. Flexibility of the tire or different setups, should not be too much of a concern, because the requirements must be met at all times regardless of wear, pressure, expansion, setup, etc. So you'd have to leave a margin of error (a realistic engineering challenge is to know how much margin you need).
Measuring width ways will always be a challenge, because of camber, which is why I've use terms like "innermost". So you would, as you say, take a plumb line to the the ground.
Wheelbase measurement is the same as current rules. The trouble with wheel centers is that it either requires specialized equipment, to make sure you are properly centered, and would be affected by toe angles. Additionally some competitor's wheels don't really have any centers to speak off, so that would be a real struggle.
What would potentially be interesting would be to come up with a simple and cheap design for a measurement tool, with four cornered adjusters that sit on the ground and tighten to the point of contact around each tire, attached to a graduated frame that sits flat under that, from which you can read all the required measurements. The specifications could then be sent to all teams so they know exactly how they are going to be measured. But I think that could be a bit elaborate, and would face resistance form some event organizers.