to me, there is no difference down to 1.1.1 or 1.0.2, either of one has to be done cause there is no direct jailbreak for 1.1.2 otb. Plus you would have to jailbreak/activate 1.1.1 (via exploit etc) using other activation methods aswell.
Steps on a Mac (in short)
1. Connect OTB 1.1.2 iPhone to Mac
2. Start iNdependence 1.3.1
3. Click "Enter DFU mode" in "Firmware" tab.
4. Quit iNdependence and start iTunes 7.5
5. Option-Click Restore and select 1.0.2 firmware file (1015 error on the end)
6. Quit iTunes, start iNdependence
7. Hit "Activate Phone" in tab "Activation/Jailbreak"
8. Hit "Install SSH/SFTP/SCP" in tab "SSH"
9. Hit "Pre Firmware Upgrade" in tab "Firmware"
10. Quit iNdependence, start iTunes
11. Option-Click "Update" (not Resore) and select 1.1.2 firmware file
12. Quit iTunes, start iNdependence
13. Hit "Activate Phone" in tab "Activation/Jailbreak"
14. Hit "Install SSH/SFTP/SCP" in tab "SSH"
15. Install turbosim sw and applesaft via sftp.
16. Start Terminal and programm Turbosim
17. Install optional stuff (Installer, BSD sources, carrier plists)
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iPhone 4 factory unlocked, iOS 4.3.1, jailbroken
iPad Wi-Fi + 3G (1G), iOS 4.3.1, jailbroken
out of curiosity (i trashed my iPhone switching 'phone off' with iToggle <= don't try this unless you're bored or stubborn, it's pretty safe to render your phone utterly useless with no reasonable option thru ssh to reload the commcenter), i followed your instructions up to #5, where i was left with an error 1013 (spot the difference) and neither iNdependence 1.2.5 nor 1.3.1 were able to kick the phone outta that state because the firmware files weren't accepted. that said, those files worked and do work with the guide posted here, so they're not the source of the problem.
this is not to argue about anything, just a report. also nix für ungut, meister.
Factory unlocked iPhone 3GS 32GB (MC133ZA), 5.13.04, iOS 4.0.1, jailbreakme.com Unlock
dev team & jailbreakme.com donation supporter
a 1015 or 1013 error is the same basically one is if you downgraded to 1.0.2 the other 1.1.1, but both tell you you have a baseband on the phone that i not a match with the firmwware, nothing else. Remember that when you downgrade it affects the Firmware not the baseband, the baseband always remains the highest that was installed on your phone.
being OTB 1.1.2 the baseband is 4.02.13_G, which is not the one for 1.1.1 or 1.0.2 these last have their equivalent basebands. the 1013 and 1015 simple tell you that your baseband firmware is not the one that should be there. Not a problem, nothing that will hurt your phone.
Independence 1.3.1 works fine with any 1.0.2, 1.1.1 or 1.1.2 iPhone and the latest iTunes 7.5, for Activation/Jailbreaking if you follow their instructions carfeully