Single-engine plane with long range flyable in Europe
There are definitely aircraft which meet some of your criteria, namely range above 800nm and can be flown IFR. I'm not going to list them all, notable examples would be the Mooney M20 series, the Cirrus SR22, Cessna 182 and Cessna 210. No doubt there are more. The issue will be cost, you can find older M20s and Cessnas for your budget, the cheaper they are the shorter time the engines have until they need a costly overhaul and the more work they'll need.