I've no idea as to wear rates of the tyres but I'd not trust 2.5mm to deliver 2000 miles. The question is, would you be happy ridding the run home from the tunnel, fully loaded from a trip, with it pissing down, on less than 1.5mm of tread depth? I know I wouldn't!
When I've been on trips and people have needed tyres, there's never been a real issue in getting them and the price has always been reasonable (except in Switzerland!!!) but it always takes the best part of a day out of your trip. That's time I'd rather have for riding having paid in time, effort and money just to get there.