Flat fielding without a big white card...

I reproduce paintings with photography and I'm running into a problem... The larger the artwork the harder it is to get the lighting even right across the painting. The usual solution is to use flatfielding with a huge piece of card, held up in front of the artwork. Quite often this isn't possible so on my last capture I resorted to putting a colorchecker classic as a reference in the centre and in all 4 corners of the painting, then using gradients in photoshop so even out the light as best I could. It was fiddly and even then it was tricky to balance the light effectively.

Does anyone know of a plugin for photoshop or a an efficient technique to flatfield in this way?