Welcome to the forum. I was also thinking about doing a dolomite build except im still working on my lowrider build atm. I found this on youtube a while back and that is where I got the idea to maybe do a dolomite build. Maybe you can get some help from the person who built it or maybe some ideas on mounting the engine. If you read in the comments the person who built the bike has his email in one of the comments where he was saying somthing about if anyone wants to know how he did it to email him and he will be glad to help. From the looks of it on the front he just built a bracket to offcenter it and also in the back has a custom bracket and just drilled through the frame and bolted it through the clutch case/cover. On the back for the sprocket he used 3 rubber gromments on the one side to make the sprocket stick out enough to line up with the drive gear/sprocket. There is alot of good info in the comments also.
The Mongoose Beast dosnt have the gears, im sure you can get it to work some how.