1) I love the Germans because every little part has a part number cast into it. Your core extensions have a part number on them (cast into the side) so you can tell exactly what they are. The base cores have the part number cast into the bottom of the "foot" of the core. Verify that all your cores are correct before you start chasing other problems. In a lot of 3 different tank systems, I have 3 different base cores which are just slightly different in length so that could be tripping you up.
2) I'm looking at the Jobo CPP2 manual now. The 2850 drum system is composed of the 2830 print drum and 2870 print drum Extension Module. The closest film tank equivalents are the 2593 tank system which is composed of the 2553 film tank (aka Multitank 5) and the 2560 film tank extension.
3) The 2870 print extension module and the 2560 film tank extension module are definitely the same thing. I received a 2870 yesterday and it builds up on the rest of the 2500 system just like Jobo says the 2560 should and the cores all fit as claimed, etc. So we know your 2870 isn't the issue.
4) We're now into the realm of educated guessing. Looking at the CPP2 manual, the picture of the 2850 print drum system looks slightly different than the picture of the 2593 film tank system. Specifically, the extension and base drum of the 2850 look almost identical in length while the extension on the 2593 is much longer than the base tank. Since we know that the extension (2870/2560) is the same, that means that the base drums must be different, with the print drum being slightly longer than the film tank. Since my CPP2 manual was printed in 1999, Jobo has released a new film tank that the manual doesn't cover called the Multitank 6 which is slightly longer than the Multitank 5 (2550). The Jobo USA website lists the part number for the Multitank 6 as 2560, re-using the part number they used to use for the film tank extension. Bad Jobo! Then on the very next line, they list a Multitank 8, which they also claim is part number 2560, so someone is making a mess of this. I would be very curious to see if the 2830 print drum you have matches the new Multitank 6 (2560) film tank. Either way, shame on Jobo for breaking their own numbering system and making the whole thing a confusing mess.
5) Jobo's own current literature for tank combinations, volumes, and cores still uses 2560 to refer to the film tank extension module.
6) If I had to take a wild guess at what cores the Multitank 6 needed, I'd try a 04044 base core, a 04045 core extension, and a 04073 stubby core extension. The 04073 stubby core extension looks like it would perfectly account for the length difference between the Multitank 5 (2550) and Multitank 6 (new-2560). This is based on one picture of the Multitank 6 and one picture of the stubby core extension I was able to find through Google Image search. This, of course, is making the assumption that your 2830 print drum is really a Multitank 6/new-2560 in disguise (which seems very likely).