Mosaic with different background levels

Taking the images for my mosaic of the Heart Nebula took a long time (several weeks). And as a result the background levels of the different panels were quite different (mostly because of the moon). This was most noticeable in the OIII channel:

Here is mosaic of them without modification:

The first advice that I found was to remove backgrounds as much as possible using ABE or DBE. That made it better, but the differences were still very noticeable.

On one thread in the Pixinsight forum, somebody recommended to use LinearFit to equalize the levels - but that did not work at all for me:

The histogram got completely squished...

On another thread, somebody mentioned AutoHistogram:

The usage is fairly straight forward: select the image that you want to use as a reference image (preferably the image with the largest range) and click on "Set As Active Image". This reads out the median pixel value of the selected image to be used for the adjustment.

Then you just apply this process to all the other images:

Doing this to all images and combining them with GradientMergeMosaic results in:

Yei! That looks much better! I had to play with the Feather Radius to avoid a pinched star, but apart from that it was now straight forward.