[werk_ag]

I already thought about this and I like the idea - do you think the battery holder should also be integrated on the pcb or not? In my opinion it nearly gets to big then.

I thought about that too. Having the battery holder integrated on the PCB, will produce a more compact and possibly easy to assemble unit, but it have the disadvantage of largely increasy the cost of the pcb, due to the extra size. So, perhaps the better is option for having a separated battery holder.

Another thing is, that the 3A protection boards I found never have holes to mount it on a PCB - does anyone has an idea how to mount them elegantly?

Sorry for asking, it should be obvious, but what is on this module? It seems a bare pcb, surely isn't.
Do you have any link for it?

(I thought for a few seconds about designing it from scratch but all the smd soldering and testing I think it's not worth it)

I fully agree. Whenever there are available already made modules for anything, its always cheaper using them, than designing from scratch.
On this, even there are interesting things: At least on eBay, a PI RTC module, it cheaper than the RTC chip included on the PI module.