Short answer: Drop to the 25mm. Your frame cannot support a 28mm tire. Alternatively, get a touring bike. (everyone needs more bikes!)
If you are going to be 'loaded', a 28mm may be more likely to 'balloon off' your, most likely, narrow rim in a hard/fast corner than the 25mm.
And the wider 28mm may be more likely to shimmy with load. (lots of references from the 'touring crowd' on this phenomenon... here's one https://janheine.wordpress.com/2012/01/30/the-downsides-of-wide-tires/) Personally, I don't think that 28mm would be instantly unstable in your case, but the 25mm would probably impact your overall riding less. However, the 25mm will probably require a much higher pressure than the 28mm would, so you may have to have a special high pressure pump available on your tour while the people running 28mm or 32mm tires won't necessarily need (as for spare tubes... it is possible to get 25/28mm tubes.. although the 28mm-32mm is more common here in our shops).
My thoughts are that moving the rear axle lower in the frame will create a 'moment arm' in the rear-dropouts that the frame was not designed to handle... so while you could put some bits of metal in there to space it down, that could cause a failure of the chainstays, seatstays, or the dropout itself. Not saying it is impossible, but I would expect that there would need to be stiffening (e.g. more material added as a brace) in the dropout area... and a new Rear Derailleur mount along with addressing a possible problem with chain-to-chainstay clearance (or lack-thereof) on your specific frame. And, lastly, since you are most-likely a roadie, it'd look funny, even if the adapters are painted to match your bike. For inspiration, see what these guys did to move the rear wheel: XtracycleConversion (not exactly what you wanted to do, I'm aware, but see how they treated the rear-dropouts? they only applied upward force to them and further braced against the stays... your application wouldn't need quite so extravagant bracing, but that's the idea...)
This is one of those cases where a steel frame would be easier to modify/brace than a CF one. I can envision how I'd do this, but it'd be an effort on par with just buying a $1500 steel bike (something like a pre-built surly cross-check or their steel road frame) and selling it at the end of the tour. Your alternative of running 25mm tires is very attractive--especially cost-wise.
I'm not going to do more than mention that I'd also be concerned with what the handling and ride qualities of the resulting modified bike would be. Changing the steer-tube angle, even a little in relation to the rider's weight can make the bike wander or over-stress steerer/fork. (the steerer/toptube/downtube area is already high-stress for the materials there)