If you just want to heat the exhaust up, you don't need a small heater, you need
DEI.
At a high level, I agree with you - your thoughts are on target and would resolve the issue. My personal opinion is that the only issue with the existing systems are that a) the pump doesn't provide enough pressure, and b) there is no check valve / the pump shuts off. These 2 combine to allow exhaust byproducts into the air channel.
But, I would also question whether or not your proposals would really be that inexpensive to implement and would be effective. Specifically I'd be concerned about the length of time that the newly introduced air has to complete the combustion before reaching the pre-cat O2 sensor. In order to port the air in at a location that is convenient you'd need to be close to them and it may not provide enough time. Moving it upstream far enough to be effective would obviously work better, but would also increase the price tag significantly and likely would make it more expensive than the presently available software upgrade.
d-