Jim, I agree with Toyota. The MAP enhancer and the O2 are completely different animals. Running a MAP without an EFIE for your O2 will probably be detrimental to your over all ability to make gains. If i were only going to run one it would be the EFIE. By running just the MAP you are telling the ECU that the engine is not working as hard and does not need as much fuel. Then when the ECU leans out your engine the O2 see's a lean condition and richens the fuel mixture to get back to the 14.7 to 1 ratio it is programed to maintain.
You have two fuel trims to worry about. Long Term Fuel Trim (LTFT) and Short Term Fuel Trim (STFT). To simplify how this works the STFT is for the most part the table in your ECU that determines the amount of fuel that your engine needs. It compares the LTFT with sensor data to determing the length of time that your fuel injectors stay open. By running just a MAP you are setting the LTFT to a richer than normal setting. Your ECU is getting modified data from the MAP telling it that your car is not working as hard as normal needing less fuel as the air flow is lower. Then the O2 is sending a lean condition signal to the ECU telling it to richen the mixture. All this together is telling the ECU that your car needs more fuel per pound of air to maintain a 14.7 to 1 ratio. This rewrites the LTFT ro a richer table. Now as your ECU compares sensor data to the LTFT your STFT will now have a richer setting and you defeat all the gains the HHO might give you,
Sorry for being so long winded but I have access to some of the best techs and factory rep's and have been picking their brains about this for months. Beleive it or not this is the short story on how this all works.
I strongly beleive that there are just a few reasons most people fail with this.
1) Just not enough HHO to help.
2) Improper MAP/MAF EFIE enhancer combinations.
3) Impatience with adjusting the enhancers. Too big of changes to the signals from the sensors will confuse the ECU. The tables do not figure in enhancers to their calculations.
4) Running the vehicle without enhancers or HHO or both once the tuning has started. Again sending confusing data to the ECU.
Hope this helps.
Larry