Driving on your own
When there is nobody else in the car with you, nobody can object to your choice of music. You can play Allan Holdsworth, or even the Carpenters, and you are free to turn off the radio when Bon Jovi comes on.
On the piano it is straightforward to play sustained chords with your left hand while you play the melody with your right. Even if you are not going to play the tune like that in the end, it gives you a logical place to start. On the guitar you cannot do that. In most cases you will have to think hard in order to come up with a fingering that allows you to play any combination of the notes from the melody and the chord simultaneously.
My approach is essentially based on the techniques used by Pat Martino in his tune Country Road (transcribed, and included on CD, in his book Creative Force Part 2). After having learned to play this tune, badly, I realised that you can make a guitar sound 'like a band' 1) by using only a few carefully selected notes from each chord, and 2) by occasionally playing several sustained notes at the same time.
The central issue to tackle is the idea that soloing and playing chords are mutually exclusive. In a band, the distinction is usually clear-cut; you are either 'featured' up front, playing the melody or a solo, or you are 'comping' in the background while the main focus is on somebody else. In a solo arrangement, however, you have to take care of both at the same time. This is difficult to do, not only technically, but also mentally because your brain has to work on two parallel levels simultaneously.
Just The Way You Are (mp3, pdf, tef) by Billy Joel is a beautiful tune with a strong melody line and a brilliant intro. My recording of this tune is supposed to be complete, without the implied repetitions that are inserted by default in jazz. It is relatively long, more than two minutes. I have introduced small variations in the sections that are repeated. When you have a singer, you don't need to worry too much about the first verse sounding exactly like the second since the lyrics are different. The instrumental version, however, quickly becomes boring if you don't make an effort to avoid repetition.