For weird shapes like this, I sometimes use a tramping pack (hiking pack)
For a road wheel I'd use two reusable velcro cable straps to secure the top of the rim to each shoulder strap on the pack, and that's all. Wheel hangs there under its own weight nicely.
A unicycle has a crank on either side, which would likely poke you in the back. Could you secure the unicycle's saddle at shoulder height, with the nearside pedal in its lowest position, and get it under the level of your saddle? A folding or removable pedal would be awesome if you already owned one.
Here's me carrying a balance bike on a pack:
It used to be common to ride your bike to a race, with your weekday wheels on the bike and your good racing wheels on stanchions. Perhaps there's a way to support the unicycle in a similar way?
Photos from https://www.renehersecycles.com/spare-wheel-carriers-for-cyclocross/ Toe-overlap is very bad apparently.
When I tried something similar, I had the spare wheel much higher. The bottom of the spare was velcro-strapped to the fork, just above the main wheel's axle. I had the spare strapped to the very tip of the dropbar's hook, and a third strap at the front-edge of the drop. This triangle mitigated the spare wheel-s potential for wobble, but did make that side hand position tight.
If your unicycle has a smaller front wheel than the road bike (likely) it may leave you strapping the uni's frame to your bars.
A third option might be to unmount the wheel from the frame, and treat it as two separate pieces.
The bare frame could sit on a parcel rack, and it's fork legs could straddle your seat tube and go forward, beside the top-tube. This would leave the saddle sticking out aft. Then you've got a bare wheel and cranks to deal with, potentially easier.
This could be a good excuse to fit a front rack to your bike, a radonneur rack. Put the wheel on the front rack, strap the frame to your handlebars, and have the saddle up near your shoulders. Not ideal in a crash situation, but since its all attached before the head tube, it will all turn with the handlebars.
You have a rear rack, so perhaps all you need is a hitch that has a vertical slot to accept the unicycle's seat-post. This could leave the wheel on the road rolling, and pulls it by the saddle's underside.
The hard part is making sure the wheel stays vertical-ish, so it tracks properly.
This isn't going to work - your unicycle likely can't reach the road from there.
Second version of that might be a flat plate on top of your carrier, with two vertical posts. One sized same as seat post for the frame to rest on upside down, and the other with an ID suitable to hold the seat post.
Perhaps strap the wheel to one side of your carrier, or put it in a pannier bag, with the frame poking up vertically on the other side.
Last resort - leave the bike at home and ride the unicycle. Perhaps when confidence builds it will be easier, or split the difference, drive the car most of the way, and unicycle the last mile.