Hi there Sarasalmus, the problem that you are seeing sounds more like an amp/voltage drop/ starvation, rather than a rf infiltration issue. the setup that i run in my mobile is similar to power output and amp draw as yours is, and i too experence those same symtoms from time to time, mostly when the air is on. i see that you mentioned a "stock" altinator, i am wondering if you have researched upgrading to a higher amperage one for your model vehicle? i see that you didn't mention what type of battery that you were using, and or how old it is? i see that you have done the rewiring of the main power feed and bonded the vehicle. i would recommend running the ground wire directly to the battery to ward off potential problems, it also would not hurt to ground the radio to the steel trans hump in the floor with one of those ground straps soldered to one of those thin eyelet connectors that can be mounted to the so-239 connector on the back of the radio. as far as the stereo goes, not much can be done to keep the rf out of that. that is one of the unfortunate consequences of running a high power hf rig in the mobile, it is usually one or the other.
i am not sure if your vehicle has all power options or not? a full sized vehicle with all power options will draw somewhere between 40 to 45 amps nominally. when you start overdrawing the "reserve capicity" of the alternator/battery you start to rob the needed power for you vehicle to operate propperly, pulling down the voltage on the sensors and computer. which is why the idle drops when you key up, as the IAC and other components are not getting the propper voltage they need to operate correctly. you also have to factor in the 20% drop in power from your altinator when it is hot. i see that you said that it does not pull down the motors rpm all of the time, so you may want to try this. pay close attention to when this happens and see if it correlates to when you are using the radio at full output, such as on ssb with full audio output. as it is very possible that this is only happening when you are using the rig at maximum draw.
way back before i installed my setup, i upgraded the altinator from a 120 amp to a 170 amp, upgraded the battery to a yellow top dual post, and as you did upgraded the charge wiring from the altinator to the battery with a 4 guage wire. i also bonded the vehicle( doors to body,hood&fenders to body, body to chasis, motor and exaust to chasis...etc.) by the time i was done i used almost 50' of 5/8" tinned ground strap. you may want to try this approach and it should improve, and or eliminate the symptoms that you are seeing. not sure how much $$$$ you want to invest in this, but i would recommend going to a custom altinator like the kind they use in the car stereo industry. i have seen them in the stock oem cases but are capable of 200 amps and higher at idle speed, with extra heavy duty voltage regulators to help maintain the voltage with less drop under load. at lest for me, i know if i would have used one of these in the first place i would have eliminated the symptons completely, if i decide to install this setup in my next vehicle i plan on installing one of them. hope this helps, let me know how you make out.