So much to suggest, jgf.......
First thing is, winds change, as Webb indicates. Beyond that. air pressure changes (meaning that height readings become inaccurate) and compasses deviate (leading to you getting off course). I'm frankly surprised that, using your 'method,' you weren't up to 1,000 nms. off course, instead of just 300.....

As Webb says, the simple way to stay on course is to switch from 'NAV' to "GPS' on the autopilot. That way the course will stay right. But at the expense of the whole flight being as boring as watching paint dry.........
The way to deal with air pressure and compass variations is to press 'B' (for 'barometric') and 'D' (for
'deviation') from time to time. But I'm afraid that that doesn't do much to alleviate the boredom.
My own solution is not to bother with marathon airliner longhaul trips and to make shorter (1,000nm.-2,000nm.) trips in lighter aircraft. And, for good measure, mostly to make 'round-world' trips in them.
Beyond that, I leave 'GPS Hold' alone as much as I can and use 'traditional' VOR-to-VOR navigation as much as possible. VORs usually have a 200-mile range, so it's necessary (and also fun) to plan your trips as far as possible in 'under-400nm. 'legs' as far as you can.
Finally (in my opinion, and I know many will consider it heresy!) to Hell with not using 'accelerated time' on occasion!

I tend to concentrate on takeoffs, climbouts, course changes, patches of bad weather, approaches, landings, etc. - and don't hesitate to use say 4X acceleration on the long boring bits.
At least I 'see' the whole flight that way - and don't face the risk of waking up smelling smoke and realising that leaving the 'puter on has set the house on fire......

Beyond that, I find the whole process of planning and carrying out round-world flights in under-2,000nm. legs in smaller (and therefore basically-unsuitable) aeroplanes endlessly satisfying and absorbing; especially using different dates and 'real weather,' and having to cope with all sorts of airfields, including plenty of under-equipped ones.
Don't really have to say much more because, years back, I wrote that approach to FS up in a 'tutorial' which Simviation were kind enough to put on their site. It provides a lot of detail on VOR-to-VOR navigation, route planning, fuel conservation etc. Click on "FS2004 Round The World in A Prop" (sixth one down) if you're interested:-
http://simviation.com/1/browse-Adventures-128-2PS - about
"Flight analysis showed I had flown in a large arc rather than a straight line', you have to blame a guy named Mercator for that. Way back, he devised the "Mercator Projection' - which shows a flat world on a rectangular map. In fact, of course, it's a sphere - so that the 'true route' from A to B follows a curve, not a straight line, on Mercator's map. The navigators' term for that is the 'Great Circle Route.'
With the result that, among other things, on his map, flying the shortest route round the world from Australia to Australia, you'll find yourself flying over Northern Canada.......