I have an x-vert and it is a fun plane, however it does get wonky A LOT on transitions, and often crashes for no good reason when switching to and from vertical mode.
I couldn't find an answer directly on how to do it with off the shelf parts, but looking into some of the knock offs might help. Some models I found were the Mirarobot M600, XK X420, and Eachine Mirage E500 (found all on banggood). I'm guessing documentation for them might tell you what FC you might need and how to set it up. If they use a dedicated board, you might be able to buy one for much cheaper than the x-vert board.
I do remember someone from the RC Groups thread on the x-vert building a replacement fuselage from foam board - found it here https://www.rcgroups.com/forums/showpost.php?p=40714111&postcount=5342
you might be able to "borrow" this design for your project.
Another place to check out VTOL ideas would be on Tom Stanton's youtube channel - he's a college student who does fun engineering projects - he has done several VTOL aircrafts in fact there is even a playlist of them. https://www.youtube.com/playlist?list=PLj3Bh6Krv9CXC8L8c3bPgonU7mtuRoIIa
His units aren't really similar to the x-vert, but there might be enough information on how he solved problems that it might point you in the right direction.