hmm... it seems the install script was not able to delete temporary install files on your Windows partition. What filesystem are you using? NTFS or FAT32? Try to install AmiKit to different Windows filesystem partition. If this doesn't help, try this please:
Install AmiKit as you described and at the end of the installation wait at least 15 seconds before restarting AmiKit so the files have time to store on your HDD. Restart and if the the installation screen appears again, then QUIT the emulation.
Assuming that installation of your OS3.9 system files was successfull and the only problem is that AmiKit script was not able to use regular startup-sequence instead of the installation startup-sequence, you have to do this manualy (by using Windows).
(overwrite the old file there)
btw. if you're skilled in AmigaDOS, you can take a look into AmiKit\S\Startup-Sequence2 to see what's going on during the installation of AmiKit.