With regards to the holes. You don't specify the length of the hole or the tolerances you are needing to comply with only "This operation requires a level of precision that Is at the outer limit of my skill set.".
First, as stated, use the tail stock. It will provide the best support.
Here are the steps I would start with.
1) Ensure that your tail stock is properly aligned with the chuck. This should be done with an
Alignment Tool and a test indicator to make the adjustment. When I do this, I try to get it into the tenths. Of course zero is best but not as easy to do with tail stock adjustments.
2) Use a centering drill to start your point of entry. I will assume that the face has been trued. When starting do not apply heavy force, touch and back to get things started. Light touches will help to prevent wondering of either the bit or the part.
3) You don't state the size or depth of hole, I would start with an undersized short shank drill for rigidity. The shorter the better.
4) Follow this with a larger drill diameter but again with the short shank. Be sure to not drive the bit, let it do the cutting, clear the chips often and lubricate with cutting oil. I like tapping oil.
5) Deapen the hole to the desired depth. If the depth is critical, again it is not called out, you can use a dial indicator. You can rig a collar on the quill of the tail stock that you can have the dial indicator rest against for measuring. Either use your mag base dial or you can get dial indicators with a magnetic back for this. Another item is to rig your tail stock with a single point
DRO. There are other types too, all require some fab to mount.
6) Finally, complete the hole with your reamer, again clear the chips often, go slowly and use cutting oil.
Also ensure your drill bits are sharp. If ground properly, you will see even chips coming from both flutes. If they don't it will cause the drill to wonder.
I hope that this helps.
