Hey Paul, don't trow your 3DS just because your 3 screws are striped,
On this link bellow there is some one who just got a problem similar to you, I would do as the member Bob lathim did and if you manage to remove them without scratching or destroying your case, the buttons bellow are probably out of contact and you would need to replace them and clean the gold pads inside the console ( to do so use 99% alcohol from a pharmacist), dust dirt sweat from your fingers can slip inside and do some nasty things.
Link: How do I unscrew a stripped screw on the lower case?
If you manage than to open the console without destroying the case than you are good to go for a champagne bottle well deserved, and to reassemble trow the screws and purchase a cheap screws set on ebay : http://www.ebay.com/itm/Official-Authent...
but now If you destroyed your case you would need to purchase a new one some were ex eBay: http://www.ebay.com/itm/Authentic-Ninten...
If the link above fails and you still dont mannage, you will have to appeal to strong methods. Wen I try everything and there is nothing more I can do, I use a driller with a special ultra thin metal mesh and I would drill the top of the screws taking really careful and going really slow till you see the screws are not holding any more, if you did just enough, there should still be a little end tip that you could pinch and rotate, to extract the screws out of its socket, but do try everything this is insane and it can fail. (and off course I wont take any responsibility if you try. xD), you could intentionally try to cut around the screws using a cutter (be careful to not go deep if you go deep you will destroy the mother board screen or what ever its on the way), than with a pince you would just need to manually turn them out. (easier and better than a drill)
And if you do use the drill technique and it works, you will need for sure the screws set, and probably a lower case.
Cheers and good luck,