I had something like that happen to me years ago. I had just finished a Kalt Baron 20 in a Jet Ranger fuselage (helicopter). Was out flying it the second weekend, and some guy hassled me "How much". I did the same thing you did.. pulled a monster number out of my butt. A stack of $100 bills later, and my gorgous little red white and black jet ranger was never seen again
Likely hanging in someones office to this day.
As to the initial post....... I've had a handful of folks email me recent about doing this. In short, if this is going to be a "lets see if I can do it" project, then have at it. On the other hand, if you are considering this to get that "little extra bit of speed" from the Patriot... probably not worth it... you can set up a side exhaust engine with just as much power, and the plane will be just as fast.
Use that Webra 50, put a jett muffler on it....... 9x8 prop.........have fun.
If you chose to proceed with the RE.....
Using a RE engine and building a custom upper deck and canopy (as noted above) is likely the way to go if you want an enclosed pipe. Search back in the posts here a bit. The questions has been asked before, and we had a few photos of other RE pattern ship installations. (looks for photos of an EU1-A, Arrow, XLT, Escape, Citation.
If you do want to use the SE engines, you may consider rotating the cylinder down 35deg, and running the pipe semi-enclosed under the belley. (Look for info on the dave brown / great planes Illusion - pattern ship circa 1985). Nose gear installation may be tricky in the patriot, but not impossible.... has to be offset to one side a bit, with the header hugging the other side. (Search for photos of a Conquest 4, Aurora 60, Summit, Illusion for ideas on the offset nosegear)
Bob