Went through this exact thing two days ago.
Take your pin out and find the least "pointy" end, thats the end you want touching the slot in the takedown pin.
If the least pointy end still has a flat tip or a tiny ridge like mine still did, 3 minutes on a needle file ended up making it work perfectly.
400 to 600 grit sandpaper wetted with some lube might be just perfect for this.
Before I screwed with mine, I had to use a punch and hammer to get it out. The problem is the ridge at the tip of the pin, Or the ridge in the drilled hole located at either end of the takedown pin.
The latter being fixable by taking a small drill bit (by hand) and "countersink" the holes in the takedown pin.
But of course you want to modify the cheaper part first, the detent pin.
Good luck, this is hardly a problem.