You have the right idea, it is ok to change the 'scale', but what you are doing is not quite correct. You need to stay in the A Major scale, but when you change the underlying chord, you can start the scale on the root of the chord.

Example, when playing an A Major chord, you want to start on the A. When you change to a D, you still play the A Major scale, but start on D instead. This is the Lydian Mode. When you change to E, it is the Mixolydian Mode.

The reason that it doesn't quite sound right when you play is because you are effectively changing the key by changing the scale you use. An E Major scale played over an A Major progression will not sound quite right because some of the notes in the E Major scale clash with the A Major key that you are playing in.

A Major scale - Ionian Mode - A B C# D E F# G# A
- Lydian Mode - D E F# G# A B C# D
- Mixolydian Mode - E F# G# A B C# D E
D Major scale D E F# G A B C#
E Major scale E F# G# A B C# D# E

By comparing the three major scales, you can see where the notes don't add up. However, by changing the Mode, you stay within the same scale, you just change the starting point.

I would recommend you read up on Modes to get a firm grasp on what you are trying to accomplish. I think that you will find your playing will sound awesome if you can understand the Modes.

I hope this helps.