Do you have Photoshop?
Consider setting up Actions in Photoshop to add borders and overlays. (This will require some work.)
Export the images from LR to a folder, which can keep your filenames,
Then run the Photoshop actions on the whole folder of images using batch processing.
Admitted- the Print module is ok for one-off or a few images, but having to rename many is a pain!
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Just use your PNG border file as a Watermark in the Export module by setting the water mark to FILL the frame. If you don't want the PNG border cover part of the photo you can use the SCALE option in transform to add some area around the photo.
Thank you for your reply. Yes I had thought of a pshop action but was trying to find a quicker solution. Thank you!
Aaah legend! Yes! Thank you Bob! That works - I just have to crop them all perfectly first as I don't have the option to slide or scale the image inside the border but that's a small price to pay for retaining the file name. The watermark png overlay does the trick!! Cheers.