My oak experience isn't with burr, but they have relatively fragile taproots at that stage of development. I have successfully extracted some from a similar situation by sssssllllloooowwwwwwllllyyyyyy submerging the pot in a 5 gallon bucket until the potting mix and saplings floated themselves out of the pot, allowing me to separate them.

@LibertyLizard might be able to offer better advice than I can, they've been doing some oak transplanting as well.

I'd tip out the pot and gently separate the saplings. Hopefully they're not too entangled. Go ahead and replant in the ground with the same potting soil, taking care to make the holes deep enough for the tap roots. They're long!

Just an update: I transplanted them 13 days ago using both recommendations. First I slid the root ball from the pot by turning it upside down and gently pushing on it from a hole in the bottom of the pot. Once the root ball was free I dunked the root ball into a bucket several times until all the potting soil dissolved. From there I could unspool the taproots from each other which were thick enough to where none of the sprouts were damaged and all are growing well. Pictures from a week after transplant: