There are definitely things you can do, I am doing a drive training program at the moment - but it takes time and very few trainers will be able to help you effectively. I know people who have also trained it with low stim e-collars, which don't bother me as the low stim training is not painful, but because I am also training for obedience I want to work with the drive.

Without wanting to be harsh, the fact is that you have a beagle, a high drive scent hound, the instinct to follow their nose has been built into them for centuries. I would NEVER let my beagle off leash unless in a secure area, or an area we have proofed for in training for the very reason you experienced.

I know of beagles who have followed their noses across the road and been hit by cars, it is not something that you risk with a scent hound irregardless of how much they enjoy being off leash.

If my beagle gets on a scent she literally cannot hear me calling her, because she is in something called 'drive peak' where her brain is working from the lower cortext, the medulla, which is why they are so unresponsive to commands - they are 110% completely focused on the scent which is what they have been bred to do. My beagle actually gets surprised when she realises I am standing near her - when she knows I am there she has excellent recall. But if she is on a scent there is nothing I can do to disrupt her when she is in drive peak. This is why I am doing drive based training so that we are putting the control back in during those situations.

I would never try to train OUT instinct. Why even bother having a beagle if that is your goal? And IMO it is impossible to train out an instinct that has been selectively bred into a dog for centuries. I wouldn't risk it as for me, it doesn't offer enough relability as using the drive to my advantage, the instinct will always be there no matter how much you try to over power it.