How can I position glyphs within their containing box?

I don't do much work with fonts, so please forgive me if my terminology is a little off.

A client has asked me to create a few custom glyphs to add to an existing font. Two of those glyphs are for twiddles - arrows that point either to the right or down, indicating interface area that is either collapsed or not.

The two twiddle glyphs need to be positioned so that it appears as if they have an axis of rotation in the same spot. They don't actually rotate, of course, but, by clicking on them, they swap each other out instantly, giving the rough appearance of having rotated.

The font they are being imported to is a monospace font, so the bounding area for each glyph is exactly the same.

I am using Inkscape to create the shapes of the glyphs in SVG format. I then import the SVG files to FontForge. However, I can't find how to control where in the bounding box the glyph should be. Also, I can't seem to get any kind of grid so that I can ensure two glyphs are oriented around the same spot.

I am willing to use different software for font editing, including paid software, if this is a matter of getting the right features.

In any case, though, how do I position a glyph within the bounding box of a monospace font exactly where I want it, and make consistent positions across different glyphs?