Take a look at Jake's gyro. It's a very refined lightweight gyro, based on his many years of experience.
I'm building a standard Bee myself. Afterwards I may experiment… When you have a lathe and a tool mill, there are possibilities.
After all, the Gyrobee is very basic, and the standard parts used back then are not available anymore.
From what I've read, it's not such a good idea using any kind of aeromotive engine in a gyro. Especially in a lightweight machine.
A gyro engine is hard pressed and must be able to run balls-to-the-walls all the time. A car or MC engine is not built for that.
Car and MC engines are heavier. Plus, an MC engine usually comes with a gearbox attached. They both have to have a reduction gear.
You would in reality be a test pilot with a questionable power system...
The usual engine for a Gyrobee-ish machine would be a Rotax 503 or a 582 (IMHO). There are others, but they aren't that common.
I happen to have an old, never used 503 SCSI. Single ignition and single carburetor. I have a set of used carbs if needed.
But now I'm cheating - I just bought an MTO Sport. I needed that to have something to be schooled in. I might sell my Gyrobee stuff.
Or not - I don't know at the moment. It would be fun to finally build my "Time Machine" Bee... I have just about all needed hardware.
Cheers
Erik