Given the security issues (even with Mr Shapps' help) Which destination would fill a train from Liverpool (or even Manchester?) and what rolling stock?
The same questions apply the other side of the channel, of course.
Using Eurostar's solution for Amsterdam (splitting the train into two sections) with one for Europe and one for London St Pancras (followed by London to Europe) would solve that issue. If you only have 6 or 8 coaches of a 374 to fill, that's a lot easier than filling all 16. With computers controlling the doors, that decision of 6, 8 (or 10) coaches for international passengers would be based on ticket sales.
You would need a way of getting passengers off at St P. I would suggest using platforms 5 and 6, with gates in the barrier line to allow domestic passengers out (before Europe) or in (after Europe). At the north end, you could have a bank of escalators down to concourse level.
I say platforms 5 and 6, as they would give the easiest access to the North London Line, from which the spur to HS2 could be built, and you could even serve somewhere on the WCML like Watford Junction. I've said before that you could drastically reduce the length of tunnelling for HS1-HS2 by tunnelling only from OOC to just west of Queens Park Station.
Back to Cologne, having visited there a few times (including last month), I say bring it on! If you are using the same splitting of trains as mentioned above, then you only need to partition off the end of a platform (5 or 6 at Cologne HBf). The rest of the island could remain open to passengers (including those to Aachen, Liege and Brussels). The platforms at Cologne do see a lot of use, but it's generally the central 200m or so. Most of the trains aren't long enough to occupy the full length of the platform. A quick look at Google Earth tells me that that Platform 5 is about 500m long, which is long enough for 2x7-car-ICE (2x202m) and a 100m long exclusion zone. That 500m doesn't include the little huts at the ends of the platforms, so there may be a little bit of wiggle room on that.
P5 and P6 could both be widened to make room for additional escalators from the customs checkpoint, but this may be difficult given the structural configuration. By my estimate, the iron columns that support that level are directly under the tracks. (I had a look for myself last month, wondering if it could easily be done.) Moving the tracks would cause massive shear forces (and moments) in the beams, which would require their replacement.