I'm not sure I rate the guru title (thanks Geofkaye) but I will try to help.
It just so happens I have a PE-2500PSW as well. I haven't gotten to the point of hooking up my computer to the AC inside my living quarters yet, so I may or may not have a problem myself. I also rarely use the radio in the truck (cab) when the inverter is on so I hadn't noticed anything, and I hadn't tested specifically for any kind of interference.
I just checked, and with my inverter on I get a barely audible buzz on a strong AM radio station (KGO). I tuned the radio to an empty AM channel and got strong buzz that I could hear easily from outside the truck. My inverter is located in an underbed box on the right side ahead of the rear wheels. When I turned the inverter off the buzz went away. My AC circuits are wired in through the 3 prong plugs in the front of the inverter. When I pulled one of my three plugs the buzz mostly went away. The other two plugs contributed to the buzz only slightly. I went inside the living quarters and tuned on/off the only AC light in there at the moment and it had no effect on the buzz.
All of this leads me to believe that my problem (to the extent that I even have a problem) is due to radiated emissions coming from the AC wiring in the living quarters acting like an antenna and spraying RF(Radio Frequency) noise that is being picked up by the AM radio antenna in the cab.
I have no direct electrical connection between the 12V that supplies the radio in the cab and the 12V that drives the inverter. That suggests that the problem is not feeding through the 12V power supply into the radio. That is also supported by the fact that the problem goes away when the AC wiring is disconnected from the inverter (but the DC wiring remains and the inverter is still turned on).
Your problem sounds similar, but much worse, and may not be the same problem at all.
Fortunately they make ferite cores that can be clamped on to an AC power cord. Here is one such example from a quick web search.
I am not recommending these, but they are cheap so you have little to loose by trying one. The ferrite material absorbs the relatively high frequency energy that is messing up the radio, but has no effect on the 60hz AC line frequency. It will turn that tiny amount of energy into a tiny amount of heat that you will never notice. It should be clamped on the power cord as near the inverter as practical, and you should install one on every AC cable coming from the inverter. By "cable" I mean the black, white, and green wires in a common jacket, or at least that is how I will have to do it in my application. If you have separate wires you can put a separate ferrite on each. Since they just snap on you can try them in different configurations easily and see what works best. You can even try putting more than one core on the same wire to see if you get further improvement.
You can also put a ferrite core on the DC wires to the inverter. You would need larger cores to accommodate the heavier wires though. It is also probably not necessary as your description of your problem is similar to mine in that it goes away when you unplug the house wiring.
I will go get some ferrite cores myself and let everyone know if it has any impact in my situation.
I don’t think the proximity of the DC Power wires and the AC wires is a problem. They could transfer a little RF energy back and forth but I don’t think that would contribute much to the issue, especially if you kill the RF with a ferrite before they get together.
Beyond all that, you may have an entirely different problem. You said some things in your post that concern me. I am not sure if I fully understood the topography of your layout, but it sounds like your batteries are over 14 ft. of #1 AWG wire from your inverter. The instructions that come with the inverter recommend keeping that wire short, and using #0 or #00 AWG wire for runs over 6 feet. I would also hope you are not relying on the chassis for ground return currents. You could easily have over 250A flowing through your frame, and steel is not really that great of a conductor.
Beyond the sheer resistance of the DC current path there is the inductance. Your inverter draws very short bursts of very high current from the batteries. To put this in very non-technical terms, you could have the electrical equivalent of water hammer due to the long wire from the batteries to the inverter. Aside from whatever RF (Radio Frequency Energy) it might radiate, it could also slam the transistors in the inverter and cause them to fail prematurely.
Your previous square wave (not sign wave) inverter drew much longer slugs of current at a much lower frequency and was therefore less likely to cause radiated emissions problems. There are other potential problems as you know though.
By the way, I don’t know what a “heat sink strip” is, but I suspect you are talking about a bus bar, which is just a bunch of studs or screws on a common conductor which makes it easy to connect a bunch of wires together.