You can break your journey if you enter the required number of hours into the stop-over box and thus reserve trains with a long gap between them.
Once you have finished your journey with DB Fernverkehr (long distance trains) then any Nahverkehr within Germany you have booked (IRE, RE, RB, S-Bahn section) is valid until 10:00 the following morning as far as I am aware. I think that Nahverkehr sections are probably valid for the whole day on the return leg.
To get a good price, you often need to fiddle with the connection times.
You can also do some doubling-back, so you could have a single 4-day break if that was any use.
(e.g. first break at Köln hbf, then take the second break at Köln Messe/Deutz, which will double-back through hbf - you can just ignore the trains to Messe/Deutz).
I've done 2 breaks with a 'Special' ticket, although not a 'London' one.