Is it thru glass?
If not, you already have an easy deal.
I'm surprised they allowed flash photography in the first place.
Do you have a sample photo?
Why can't you just stand further from the painting when using direct flash?
(allowing the flash to spread a bit more to cover the whole painting)
I'm particularly interested in the one using bounced flash. It should create a lighted surface that is large enough to cover the painting. If it isn't, then likely you have not given enough distance between flash and bounce surface for the light from the flash to spread out over a larger bounce area.
There are a few ways as well.
1. Just use a tripod (using ambient light)
2. This one is more novel and needs trial and error to get overall exposure and light control right. Use a tripod; Set exposure to a very long one (Eg. 8s, f16). Take the flash off camera, set it to the exposure you want. Fire off the flash in different locations of painting (Eg. left, right)
Direct flash even with an on flash diffuser would likely cause a hotspot if the painting is covered with glass. You'd need a diffuser that is as large as the painting or a bounce what is a large surface area (as mentioned above).