The really quick and dirty solution: weld the chuck to the taper. That will ensure it won't come flying off. Then you can do light milling and start making parts for a stronger/better machine!

I wouldn't bother throwing a lot of money at this as drill presses are generally not rigid enough to make 'good' milling machines. Any welder should be able to put some large tac-welds (I'd do four 90 degrees apart) on that in about 5 minutes which would prevent it ever coming off (be careful about doing too much welding as you don't want to introduce too much heat into the part).

The really quick and dirty solution: weld the current chuck to the current taper. That will ensure it won't come flying off. Then you can do light milling and start making parts for a stronger/better machine without having to buy any new bits for your drill press!

I wouldn't bother throwing a lot of money at this as drill presses are generally not rigid enough to make 'good' milling machines. Any welder should be able to put some large tac-welds (I'd do four 90 degrees apart) on that in about 5 minutes which would prevent it ever coming off (be careful about doing too much welding as you don't want to introduce too much heat into the part).