The only way I could figure out to do this is using a gamesave exploit. Use your modchip to boot to the dashboard on the hdd. You'll need evox or xbmc or something so you can ftp to your xbox. Put the gamesave exploit on your hdd, boot the game and install the exploit. Now turn the box off and pull your chip out. You should be able to boot to the exploit's install menu and finish the install up. If you cant, then this method wont work. Anyways, from here you can run Ozflash or Eurasia or something to flash your TSOP. The bin file must be 1mb and you'll have to solder a pair of points on the top and one pair on the bottom. Look around this website to find more instructions on what points to solder. Also, you can use XBTool to make a 256k or 512k bios file into a 1mb file.
I hope this helps. This is what I did to flash the TSOP in a working box I had laying around. If your TSOP is already messed this may not work.
BTW, why do you want to remove the modchip if the box works fine with it in there?