Use the smart guides. The image shows a couple of snapshots from the process. Select each letter with the group selection tool (white pointer with the plus sign). Click and drag from the bottom left or right point of a letter, position over the path, hold Ctrl to make smart guides say "path" when intersecting it, and drop there. Pick the rotate tool, click with it once on the same point and then click and drag the point on the other side to rotate the letter until the other point snaps to the path. For round letters like the G on the image below you can create a helper bounding box. First i created the box snapping it to letter N then moved it horizontally over G and stretched it a bit to fit. Then  I selected and and positioned on the path both the box and the letter G using the bottom left and right points of the box.

edit: another way that just occur to me is to find a real font containing glyphs that are boxes, put that font over your hand drawn letters and use the attributes of the type panel to format each  box glyph to match the proportions of your letters. Then copy and paste the glyphs on the path using the type on path tool. This will allow you to format with the glyph boxes on the path with things like kerning and tracking. Then you can outline the glyph boxes and use them as snapping helpers for your real letters when using the smart guides.

Here's one way:

1. Arrange your graphic letter forms in a straight line, spaced and colored as you please (no gradients, though).

2. Now, select all your letter forms, group them, and create a new art brush.

3. Now, select your semicircular arc that you want to align the letter forms to and stroke the line with the letter form brush you just created.

The letters will follow the shape of the arc, and will be vertically centered on the arc line. If you want the letter forms to set on top of the arc (like type-on-a-path wraps the type baseline around the arc), then in step 2, do this: group the letter forms and note the width and height of the group in the control panel; now, create a plain rectangle (no stroke, no fill) the same width as the group of letter forms and twice the height of the letter form group; now, send the invisible box to the back and align it with the letter form group by horizontal center and vertical top (now the box will be centered with the letter forms and flush with the top of the letter forms); now group the box and letter forms and then create your art brush. When you apply this brush, the letter forms will ride on top of the arc.

Obviously, if you want the letter forms to wrap around the underside of the arc, you'd align the invisible box with the bottom of the letter forms before grouping and creating the art brush.

Hope this idea helps ...

Ronald

True, with the "stroking" technique, there is distortion of the letter forms, but it is very slight and in my opinion it actually looks better because the letter forms themselves conform to the arc, meaning that spacing between letter forms remains constant. The horizontal strokes of the letter forms will slightly arc to follow the path and the vertical strokes taper slightly from the top of the letters down toward the "center point" of the arc. To create the "Faux Type on a Path" letter forms, I just converted the text to outlines, which creates a group of graphic objects similar to what Jason originally described as what he wanted to wrap around a semicircle ...

To minimize "bad" distortion and retain the "good" distortion, it is important that the arc segment which is stroked with the letter forms Art Brush be the same "length" as the arc segment covered by real type on a path. Look at these examples: (Note that since the text has descenders and we want the baseline of the "stroked type" to set on the arc segment, the green box [which will actually be changed to no stroke/no fill before making the Art Brush] is the exact width of the group of letter forms and twice the height of the tallest letter form from the top of the ascender to the baseline. In this case, the tallest letter form was the "h" in the word "Path" ...)

As you can see (click on the graphic above to enlarge it), in the example on the right, the distortion of the letter forms is very slight, the letter forms exactly follow the arc, and the spacing between the letters is much better compared to the actual "type-on-a-path" example on the left.

I hope this makes the explanation clearer ...

Ron

Interesting, Wade, but what did you do?