I'd check my CPS and the vacuum line for the MAP sensor. Though I've not noticed the MAP causing backfire through the TB. A disconnected or leaking MAP vacuum line will cause it to idle really bad and stall and barely accelerate.
First thing to check with the CPS is that the wires aren't cooking onto the exhaust manifold and the connector is clean. Then an ohm test.
Mid throttle bog is often an O2 sensor, but can also be a TPS. Various sensors work together, one goes bad or gives false values, it's sometimes hard to tell which is acting up.
I went down years ago and pulled a set of junkyard sensors out of an XJ the guy told me was driven to the yard, sure helps troubleshoot when your stuck. Though to tell you the truth it is the wiring or a connector as often as it is the sensor itself.
I've had mine backfire through the TB, because of bad spark plug wires and a bad distributor cap. Some of my sparkplug wires had infinite ohms, my cap was covered inside in carbon dust and was arcing.