Hummm wait a minute, Reprap gcodes should work fine on an Ultimaker 2, I've already printed some Reprap models using octoprint. Maybe the only problem is that Reprap overrides machine settings so the bed isn't leveled properly.
Your models don't seem too long to print, and as you need help, well, I can help you. You idea seems really interesting. I print a lot of twisty puzzles, and removing those seams would help for the turning quality and for the look.
Finally, I think converting gcodes from one flavor to another should be a cura feature. That would be really handy.
And good luck for your project !
By the way, I used to use cura 15.04.6 until a few days ago because I was very disappointed with the first version of cura 2 I downloaded on Linux (It didn't print well, was slow and the buttons were too big). But now with cura 2.1.2 (on mac) it's absolutely awesome, the UI is really good and understandable and clean, it's much faster and it prints well.