Just to confuse/help matters, if you check the Nuremberg toy fair thread and click on the link. there is a picture of the new Anderson road bike. This is as far as i am aware, the only road bike of any scale with a gyro. Verdict is out on it's usefulness until there has been a few in the public's sweaty palms The 1/5 and 1/8 on road bikes really can crawl at slow speed with no real wobble issues.
Your idea about the off road is more interesting though. I can only suggest you have two bikes, one with the vertical gyro and the other horizontal. You can then test back to back for comparison. To add another point, some have taken to lightening gyros to get better acceleration but at the expense of off road stability.
Don't get too deep into an idea with the bikes until you have one and are proficient ( something your heli flying will help with) Start at a base you know and go from there. Then you can feel sure when you take a positive/negative step in your developments on a bike.
And if you can get the heli gyro to be a success, there's quite a few with $$$ ready to put your way. Just find out from the bike guys like Chris Nicastro from Venom why they don't already do it, There are a number of 'flyers' in the bike game who probably already know the answer.
Hope all goes well.