I have experienced the same problem on my 1989 I-4.
According to my local electrical rebuilder, Toyota had a problem with starter engagement. My flex plate has a couple of areas where the teeth are worn down almost 50 %. The rebuilder says that Toyota came out with a redesigned gear for better engagement, and since the car was 15 years old at the time, the gear is used in the aftermarket on the denso starters for these cars. I'm not sure why your rebuilt starter would not have worked at least as well as the one you took out, but not every rebuilder may be using the improved gear.
I asked a service advisor at my local dealership if it was possible to move the engine and trans assembly far enough apart to replace the flex plate from below without removing either major assembly, and he said that one of them would have to come out to do it. So, I'll wait until I remove the engine and do it then.
According to my local electrical rebuilder, Toyota had a problem with starter engagement. My flex plate has a couple of areas where the teeth are worn down almost 50 %. The rebuilder says that Toyota came out with a redesigned gear for better engagement, and since the car was 15 years old at the time, the gear is used in the aftermarket on the denso starters for these cars. I'm not sure why your rebuilt starter would not have worked at least as well as the one you took out, but not every rebuilder may be using the improved gear.
I asked a service advisor at my local dealership if it was possible to move the engine and trans assembly far enough apart to replace the flex plate from below without removing either major assembly, and he said that one of them would have to come out to do it. So, I'll wait until I remove the engine and do it then.