I imagine that the Multi Mic uses a cardiod microphone pattern to restrict its pickup range and there is only so much that a driver can turn his head - and if he does too much while moving, he/she is risking an accident to talk to you.
I would think that getting a covering and a way of propping the microphone up somewhere in the front of the car would work a lot better if the driver cannot wear the microphone. Just as EarGear is used over HA bodies to protect them from sweat, etc., I would think that a gauzy covering would greatly reduce the amount of direct contamination that might reach the device itself but still let sound through. With the coronavirus, you are not going to permanently contaminate your device but after some period of days or weeks sitting it will decontaminate itself by the virus dying. So with the proper safety precautions, if your only use of the device is to communicate with your driver, I think you could afford to let the device get possibly mildly contaminated in use to a certain degree, then bag it when not in use, etc., and count on the virus dying off over time. The retail version of the device comes with its own charger, I think, so you could afford to let that get contaminated, too, a bit, I think. There are collapsible selfie sticks, too. What if you mounted the device on the end of a selfie stick and just extended it into the front seat over the right backside of the front passenger’s seat so that the microphone would essentially be listening to the driver somewhere up around the front passenger’s seat or the right front glove box - or if the driver were really understanding, maybe you could extend the selfie stick up along the center console, angled to point up towards the driver’s mouth. The device is capable of great directionality when it is used at about a 45 degree angle and when it is within several feet of the speaker, even if not worn by the speaker, in my own experience. Since now a lot of people are wearing masks and gloves, presumably, you’d be able to wear the same in public and protect yourself by covering the device with a sound permeable covering. Since the device isn’t breathing like a person wearing a mask, if you treat the device as if it were contaminated, always handle it with mask and gloves, bag it when not in use, and wash or dispose of the microphone covering, I’d think you’ve have more chance of catching the virus directly from someone (unless you’re always wearing an N95 mask and never touching your face) than you would from a carefully handled covered microphone. I’ve worked with screaming amounts of radioactivity both as a scientist and a health physicist and I know from using a Geiger counter and also from using surface swabs that with good technique you can just about eliminate contamination of anything but the outside of your PPE.
The other thing that you might try is suggesting to Uber or Lyft or whoever is providing your rides that it would be great if they could come up with a solution. It’s too bad there is not something like Google speech-to-text between phones, a driver speaks to his phone, a speech-to-text app broadcasts the result to your phone. But with all the people trying to help in various ways, maybe there is a techie somewhere out there who could come up with a solution - maybe it’s worth letting Google, Apple, Microsoft know that there is a need because of social distancing and hearing difficulty that needs to be solved?
I learned long ago, though, that it’s easy to have “bright” ideas but only actualizing them counts. Sorry for offering a bunch of “bright” ideas without much hope that any might actually work.
Edit_Update: Another suggestion would be to find a good source of noise like a noisy fan, a hair dryer, or whatever, find a friend or staff member in your community center who’s willing to help out, and set up a driving simulation with chairs with as much noise as you want going in the background, around you, around the helper, etc., and find out what the conditions are in which the Multi Mic can actually help out - how far it has to be from the speaker, at what vertical angle, how much to the side, if at all it can be. With myself, my wife and I virtually stood at opposite ends of our kitchen Jenn Air stovetop and I turned on the very noisy Jenn Air exhaust fan with the Multi Mic held at about my waist level pointing up directly at her mouth at about a 45 deg angle. I could easily hear her speak over the faint roar of the fan.
The other thing is that I’m wearing occlusive molds. So I can turn off my external mics and reduce surrounding noise leaking into my ear drums by at least 10 to 15 dB. You have excellent low-frequency hearing up to about 2K. I would imagine most road noise is down in the low-frequency range. You could probably improve your signal-to-noise ratio greatly by switching to occlusive molds if just for your rides to the doctor or other care that you need. I guess with the pandemic, it’s going to be impossible to get molds any time soon but at least that’s something to consider for the future.