Burrows all over my lawn!!

I have just bonded a wonderful rescue doe with my neutered buck BUT her one 'flaw' is she burrows to Australia every time I put her out. She's dug so deep I've only been able to see the few hairs on the end of her tail before. I appreciate this is normal behaviour but can anyone suggest a more garden friendly way of letting her out in the run? She has as much time as I can give her in the run before she gets to an escape level, she's not trying to escape just enjoying herself which I appreciate but I can't keep up with these trenches indefinitely. What do other people do to satisfy their rabbits needs to dig? She is out in either a double stable with multiple toys and enrichment or the run in the garden for up to 12 hours a day so I can't believe it's boredom.
She came in to rescue as a returning stray who the owner eventually did not reclaim so I suspect she's dug her way out before now, I don't want to lose her but I don't like restricting her outdoor time (there's only so long I can watch what she's up to!) advice please?

Is she spayed? You could try giving her a digging box/sand pit and seeing if that distracts her but there's no guarantee. Have you thought about putting mesh on the run floor? That way she can't dig out but can still eat the grass. If the grass is very short or if she is a rex/has any sores on her feet then you might be best putting a layer of turf on top of the mesh

Is she spayed? Unspayed does can have a strong instinct to dig, spaying can help improve this, as well as the other health benefits.

I would lift the top layer of turf, lay down weld mesh and then replace the turf. This way you'll get no problems with feet getting sore from mesh, and she can still have a little dig, but she'll be safe and you won't be filling in holes all the time! Once you've done this, you could also add a digging box, so it's easier for you and the mess is more contained.

Yes she is spayed, she is from a rescue who neuters all it's rabbits before rehoming. As a veterinary nurse it's the first thing I would have had done had she not been

She's a wee monster, she was up on a shelf in the stable this morning (all the toys she has and she's climbing shelves!) helping herself to fibafirst. To be fair she's the first rabbit I've ever met that eats them lol.