The sqr() formula fails for long distances because the omnidirectional pattern square law attenuation takes over the earth's surface curvature as the dominating factor.
I don't think you will pick up a VOR at 200nm, with the flag
not showing, on a properly calibrated VOR receiver.
Same with DME.
I have asked old airline pilots how they used to do it, pre-RNAV. They used to fly headings. It worked because it is kind of hard to miss Spain when flying say 190 (or whatever it is) from the UK
Then they would pick up a VOR somewhere... But you can't do that anymore. Any apparent loss of precision nav today, and ATC are onto you.
There are now of the shelf inertial nav (fibre optic gyro) products which are directly usable with any moving map device that has an NMEA input, but I cannot see anything appearing for less than £20k, and that is a "portable" unit. A certified unit would be a lot more.