After @drifand reminded me of Ballograf (I have a few mechanical pencils from this manufacturer, but I’m not happy with the mechanism), I just had to have an Epoca P ballpoint pen. How could I have lived without it for so long? I chose the yellow one.
Since I prefer the Jetstream refill over the Ballograf one (which is not compatible), I looked for a solution. The G2 refill is slightly longer and the hole in its plug is not wide enough for the Epoca. On Reddit, someone took apart the Epoca and removed a piece from one part so that the G2 refill would fit. Delighted, I did the same.
It’s easy: Remove the lower part, place the upper part on a piece of cloth so that the parts cannot roll away, and press the button into the barrel; this way, all the parts[1] will come out. It is very important to pay attention to the order of the parts, otherwise the assembly will not work. Remove the pin flush from the second part from the left (red) and assemble the pen (the last part can be pushed into the barrel with the refill).
But, alas … The G2 refill (in my case: the Uniball SXR-600) is still a little too long and therefore needs to be shortened slightly. Had I known this beforehand, I would have refrained from disassembling the Epoca and instead only modified the G2 refill (in this case, however, I would have had to widen the hole in the plug). But anyway: Now the G2 refill fits, and the Ballograf refill can still be used. And while I was at it, I wrapped one layer of tape around the tip so that it no longer has any play (unfortunately, this is also the case with the refill that comes with it).
Now I have a pen that is, of course, the best I have ever had 
When I look at the parts used, I think it would have been easy to design the mechanism for G2 refills. One could almost get the idea that Ballograf did this deliberately … ↩︎