Remember you pay no fuel duty when crossing borders, so it may be more cost effective to lease at a dry rate.
You sure about that? I think it very much depends on the borders that are being crossed
I'm not sure that you are going to get a rate that is particularly special for 12 hours hire. You'll probably want the aircraft for 3 days at least, so that's only 4 hours per day...less than a typical club useage. So no great reason to give you a special rate.
If you hire from someone other than your normal school/club, then you'll also have to do a checkout...perhaps an hour or so, which is likely to cost more than any discount you can agree (if any) for 12 hours.
The person hiring it to you for 2 or 3 days also knows that if the weather isn't good enough for VFR on day 1, then their aircraft may not fly at all for the 2 or 3 days, which also makes them less likely to give you a discount.
I suppose weather in Italy/Slovakia is more likely to be good VFR than where I'm from, on any given weekend, but when you need to be there for a particular occasion, you need to also build contengiency plans if the weather isn't suitable for VFR.
Probably not what you want to hear, but I think that you'll probably do no better than the rate that you normally hire for. No harm in trying though
dp
ps. Visit the Castle in Trencin for their evening tour if you are free one of the days. It's quite enjoyable.