and I want to create the same exact geometry 1/4 of an inch bigger.
Offset will round the corners:

Which is not what I want…I want the corners to be equally sharp as the original shape.
Scaling the object does not keep the right proportions…I can’t control the 1/4" and it won’t align back when I try to center the objects on a common center point:

You can’t scale by a fixed dimension. You can scale by a percentage, or change one dimension by a fixed number, but the other dimension will be changed by the same percentage as the first.
So, yes it would keep the corners sharp, but it would not offset the entire boundary by 0.25"

I did what I had to do…brought it into Inkscape and offset it there. Still required a little boolean magic when I got it back into CC, but it did scale it the way I would have expected it.

I noticed a couple of things…
If the object is symmetrical, it can be expanded using the scaling tool.

However, if it is not, Scaling distorts the image:

If you have a rectangle that is 1" x 0.5", and you scale it by 50% (x 1.5) you will add 1/4" to each end.
But you will only add 1/8" to the longer sides.

Each dimension is multiplied by 1.5

To get a constant offset you would have to scale the length by 1.5, and the width by 2
This is one possible answer, give us non-proportional scaling so we can enter different values for X & Y.
The other option would be to add extended corners in offset, rather than rounded corners.

This would not be a perfect solution, as what would likely happen in the corner by the convex end is a tangential extension (blue) rather than a natural extension of the curve (red) until it intersects the other extended sides