How does a roof replacement impact recommended timing of solar panel installation

Since you have an old car battery, the cost of damaging it by overcharging isn't much ($40?) and that would only happen if it got a lot of sun over weeks. A small home solar system might have thousands of dollars of batteries, so standard practice has long been for those to always have charge controllers.

For small systems the cost of a charge controller used to be significant so it was common to forego it in favor of simplicity. However, there are now very - inexpensive - controllers which no longer as easily justify the old practice.

If you can afford an additional $25, you might as well do it right. Also, it would come with instructions on what to do.

Am I missing anything? Is there a piece of equipment I'm overlooking?

Yes. Large solar panels can be bought individually rather than cobbled together from smaller ones. These are designed to feed from the panel as-built rather than having to be modified. Example here.

So what you need to do is find a low voltage garden light system (perhaps one powered by the mains as suggested by @longneck) then replacing its mains voltage converter with a feed from a battery pack charged by the panel. The battery packs could be central or at each light.