It looks like you have the perfect spot for a rain garden! A pop up drain will be a good fit so you don't end up digging a really deep garden. Maybe you can snake your garden shape along the edge of your yard so it doesn't protrude into your lawn too much.

I was not able to do the complete the percolation test. After filling the hole with water the first time, it took 7-8 hours to drain! So, I'm assuming that a second fill would not drain at all before it evaporated.

The drain that leads to the area I want to install the rain garden takes water from a down spout that collects about 1/4 of the run-off from the main roof of the house (260 ft2), but it is also the drain for the sump pump, and I'm not sure how to measure this. Maybe this doesn't matter, since the sump pump is not always emptying into the drain at the same time as a storm?

So, based on the size of the drainage area (roof only), the rain garden should be 52 ft2. The area that I have already dug out is about 32 ft2, so I will need to lengthen it or widen it.

Sounds like a good analysis. 7-8 hours isn't very long. I would say you have "medium" soils. Not too clay-ey, not too sandy.

Sump pump measurements are more on frequency. How often does the sump pump go on? Do you hear it every few minutes? Once a day? Twice a year?

If it is every day, or every few minutes, size your garden larger. And select plants who like the wet. I like your Iris! They will do fine!