It seems to me that you have at least three questions here. The fit of the bearings and how to layout the new part and how to make the new part.
The fit of the bearings: A bearing supply place should be able to tell you how a given bearing should fit. Some BBs will jam if used in a press fit while others are made for it. Talk to your supplier. Find a local one if necessary or work with a more distant one on the phone.
Layout of the new part: The overall outline should be easy, just measure the existing part. With no photo it is difficult to say with any assurance, but you could use the old plate with the bearings inserted in the holes. Get some transfer punches with diameters to fit the ID of those bearings and use them to mark the new locations. For the holes that have been distorted/enlarged your best bet is to examine the old holes to see which side the wear is most prominent on. Push the bearings against the OPPOSITE side when you use the punch to mark the new plate. With any luck, that may work. If not, you can do the same thing but add some shims on the "good" side of the old holes when you punch the second try at a new plate. The fit of the parts when you attempt to assemble the machine will tell you something about any errors in the locations.
Making the new part: Doing this job on a drill press is not something I would do. Holding any accuracy there is going to be difficult. I have a 20" drill press with a large table, but I would not try it there. This seems to be a mission essential machine that you are repairing. You should be able to justify the cost of a proper milling machine to management for this. An import mill can be purchased for a few thousand dollars and will make this job a lot easier. If that is not possible, I would suggest finding a machine shop that can do the job right.
As to tooling/drills, no drill bit will produce a hole that is good enough to properly mount a bearing, press fit or otherwise. You would need either a larger reamer or a boring head. I don't know the OD of your bearings but I am imagining around 2" to 4" or so, That is really out of range for drill bits. It could be done, but I wouldn't. And that also makes finishing it with a reamer a bit difficult. Reamers require drilling first and then reaming. This is a job for a boring head. And for a rigid set-up on a milling machine.
Finally, I would also consider a better, harder aluminum alloy or steel. There are hardened aluminum alloys that can be machined easily.
So the company i work for uses specialized shredders to make gift basket shred. I dissemble and put back together the shredders for maintenance. Were at the point where we need new plates that hold the bearings/gears and cutters. Ill post some photos. It uses 2 larger bearings that arent really suppose to be a press fit (incase shredder jams it wont snap anything) and after months of use the bearing holes widen due to the bearing bouncing around. Should they be press fit ? So how do i find the true center of the hole since they have became misshapened ? . We have simple tools here at work and best thing being a drill press. What drill bits ? Basically i have a blank block of aluminum and need to copy whats in the pic. All the holes as well.