If I were trying to put a square base on that alighen the bit whichever direction I pull it across the workpiece, I'd start by finding the exact center of the base. Mark center with a fine point punch of some point. Then, with the stock base still on the router, I'd put some kind of fine point "bit" in the router and center it on the mark in the square base. Align the router so the handles are square to the sides of the new base Then I'd outline the stock base on square base. Mark at least 2 points on the perimeter of the old base, then with the finest point marker you can find, mark the new square base as precisely as you can aligned to the marks on the base. Precision here critical.
Remove the old base from the router and line it up precisely to the outline and registration marks. Use a little tape to hold it in place, and triple check the alignment. Any error here will translate to misalignment when you change directions during a cut.
Next locate some punches of the same size as the mounting holes in the old base, check the alignment again, and mark the hole locations. Remove the old base. GO TO YOUR DRILL PRESS!! Now drill the holes, and either countersink or make a second slightly larger flat bottom recess for the mounting bolts. Personally, I would be inclined to use countersunk because the precision of the method would get me within 1/32 nd, and probably closer. I would not want the play in alignment the other method might introduce.
Finally, since you are using a solid base, not pre-drilled base, you'll need to drill out the opening for the bit using the Drill Press. Personally, I'm inclined to think 1/4 to 3/8ths alunimum for the square base. I'd also would use a very fine file, then sandpaper, to smooth out all the aluminum edges so it wouldn't bind.
That's what I'd do at any rate. Any other suggestions?
