How can I reach distant systems

I personally never bother with the 3rd party tools. They don't contain information about every star system in the game and there is no guarantee of accuracy of the information that they do contain.

I always do as you suggest - rotating the map around the destination so that I can see the marker for my current location (if you "lock on" to the desired destination you can use the little arrow buttons next to the destination and your current location to swap between them, giving you hints to the direction).

Once the spider web of routes has expanded out to the maximum range (currently about 100Ly), I choose a point on it that appears to be going in the correct direction. This system is clumsy, slow, and frankly not very good, but at least it doesn't involve Alt-Tabbing out to 3rd party tools.

Soon (within this month, according to their announcements), Frontier are launching an update which among other things will extend route planning out to 1000Ly, so this should alleviate the problem. Hopefully this range extension will not be a simple adjustment of the current route planning max distance parameter - hopefully better optimised path finding code has made this extension practical.

Personally I don't understand the need for the game to plan out every possible route from your current location. Like the original Elite, it could simply give an indication of how far you can travel in a single jump and leave it to the player to trigger the route planning - when they select a system as the destination, no matter how far away it is, the game should then plan the route to that system. It should be a lot faster, a lot less cluttered and a lot more useful.

There are a number of online third-party routing tools that you can use to find your way on long voyages.

CMDR's Club is the one that I use, although Elite Dangerous Central is another one that's fairly popular. Note that these tools may not work for distant, less-frequented star systems.

One technique that can help a little is as follows:

1. Click on the target system (at whatever distance), and select it to put a marker on it.
2. Zoom out until you can see both your current location (blue marker) and the destination (orange marker). Your view should still be centred on the destination.
3. Zoom in slowly until your current position disappears behind your viewpoint, and hover the mouse over stars in the foreground until you find one at a little under 100Ly distance.
4. Wait, if necessary, for the blue route network to reach to the star you are looking at. Ask the game for a route to this star. Repeat after 100Ly.

I've found that this method is helpful for travelling up to ~500Ly. Beyond that it may get too difficult to operate. It won't help to route around large sparse areas where you may have to backtrack for more than 100Ly.