Sorry to hear you're having problems getting this to print well. This file has been used a lot elsewhere with few problems (a business I deal with printed 120 for a promotion with no issues) so it has to be something to do with the slicing app you are using, your printer or the filament... all are different. I know these print really well on MakerBot Replicator 2's and 5th Generation models.
I haven't heard of anyone else printing these on a delta machine before so that could well be affecting it... but also I note you comment about the built in Raft structure. There is no Raft designed in at all. I recommend using Raft (apply when slicing the file) but it's not designed in. So that could suggest it's a slicing app issue... and only use PLA for this. ABS will not deal with the angles / overhangs well enough. Even with PLA machines need a filament fan to solidify the extruded PLA quickly enough to build features like the barrels.
I'm not sure any of this is going to help in your case as your machine is quite different to what I've tested this file on. Having said that, maybe try a print of the one with "Fixed" in the file name... the turrets don't turn but it's otherwise the same model.