Thanks to all who helped!

I got the chance to replace the starter today on my 98 accord and after a
few starts the starter got worked in and now starting is smooth.

The biggest time-waster was the right bolt that screws the starter to the
transaxle. It's in a weird place underneath a bunch of stuff so I had to use
an extender and a bending socket to reach that bolt. Other than that,
everything was trivial.

--Viktor