I. Who says the lights should be on "both sides" of the frame?
How about putting one light on the left and above the painting, and the other on the right and below the painting?
This way the reflection will move to the corners of the frame.
But as you commented, it probably did not look better. This solution needs a lot of ...
The left side of the frame seems quite acceptable, I presume it's the right side that's the issue.
Now that you've got everything other than that right side of the frame good, move, add or remove lights until you get a good image of the right side of the frame, then composite the two together taking the good from each of the images.
Remember that when you ...
The only way, I would try, is to use a soft light source, that is as large as possible and can be placed at a longer distance.
The problem that you will encounter is, that you want soft light to minimize reflection (aka glare) on the frame. This is achieved via using a diffused relatively large light with even light distribution.
Then you want to control ...