A quick excerpt from my logbooks.
AA5b
September 2011
Enstone (Oxford) --> Liege (Belgium) 3hrs 10 mins
Liege --> Bubovice (Prague) 4hrs 00mins
Shaving off the taxi time at each end, that looks roughly like this...
Great Circle Mapper
Two reasonably large adults, two folding bicycles, two people's worth of significant baggage.
That's an example of what you can do with aN affordable light aeroplane.
In my opinion, the first thing to go on your spec should be the cruise speed. If you can accept a bit over 100kts, you'll find far more suitable and affordable aircraft types for only a small reduction in journey time. IIRC, that AA5b was actually giving us about 115kn CAS, but the wind was against us somewhat.
Types I'd look at, in roughly escalating cost and capability:-
AA5b
Cessna 172 (various models)
PA28-181
C182
PA28-235
PA28-200R
I know and have flown the Jabiru 4 seater, it's great, but it's sub-ICAO, so you'll not be able to easily use it internationally, and I don't think that many exist outside of the UK and Australia anyhow. Also I suspect you won't get much product support in the USA for either the airframe or the engine.
I'd strongly recommend getting your PPL behind you first, so that you're in a better position to assess aeroplanes.
And yes, anything above about 2.5hrs in a light aeroplane is pretty gruelling. 550nm I'd do in two hops if you conceivably can. I am used to long light aircraft trips, but rarely let myself do more than about 300nm between breaks on the ground, whatever the aeroplane's capable of.
G