I thought I was following what you're saying until the last 3 lines. If you don't mind using lay man's terms for dummies like me.
Are you saying it is a good thing to have this ferrite toroid as close to the other components of the inverter or not?
In this picture would be it be a good idea to the put the toroid around the positive and negative 4/0 cables on the inverter side (red Circle) or would that cause the overheating issue that you mentioned?
Yes, good to have ferrite close to inverter (rather than close to battery), and put it around both positive and negative so it reduces radiated RF power.
Two separate issues:
1) If the inverter generates common-mode noise on the wires, that radiates. Assuming the ferrite is effective blocking the noise, the length of cables from inverter to ferrites is what acts as an antenna, so ferrite closer to inverter is more effective.
2) AC current in wire causes changing magnetic field, which the ferrite attempts to oppose. The ferrite is suppose to do this by storing and returning energy (an inductor) but also dissipates some power so could get hot with large AC current.
The ferrite is quite small compared to a power transformer, can store very little energy before it "saturates" (becomes as strong a permanent magnet as it is able to be.) A small current through it, and it can be magnetized first with one polarity then with the other; that works as an inductor. Once it is fully magnetized (all the atoms' spinning electrons are oriented one way) it ceases to absorb magnetic field from the wire, and current flows unimpeded. The current to saturate could be on the order of milliamps.
With 100A DC flowing through a cable, the ferrite would saturate and be useless. With positive and negative cables through it, The sum of +100A and -100A = 0A, no net current and the DC current (and any differential current) cancel and don't interact with the ferrite.
What the ferrite can do is block common mode current (only if differential mode is canceled by having both wires go through it.) If both battery terminals are swinging up and down together in voltage, and the battery is not (relative to earth), current will propagate as a wave. Just like in the antenna of a radio transmitter. Just like a digital signal in a wire, over a ground plane. Often, wires used to carry data are dimensioned to have 50 ohms characteristic impedance. The pair of battery cables dangling in the air (small diameter and far above the ground) could be more like 100 ohms, just a guess. Consider if the battery terminals have 1V RMS common mode on them. That is, negative is at zero volts and swings +/-1.4V, positive is at 48V +/-1.4V. 1Vrms/100 ohms = 10 mArms. That is what the ferrite sees, and its impedance reduces the voltage amplitude on the cable after it. Maybe zero +/-0.1V and 48V +/-0.1V, so less power is transmitted.
That was about preventing radiated power from an electric "E field" antenna.
3) Third issue, preventing radiated power from a magnetic "B field" antenna:
Current flowing in a loop is differential, and radiates power. That depends on how large the current is, and how much loop area. If you lay the positive and negative wires a foot apart, there is several square feet of area. The 100A DC current doesn't matter (makes a DC magnetic field) but the pulses of current drawn by switcher, to the extent not filtered by capacitors, are AC current in the wires. Choke can't help that. Inductors in the inverter design may help. Twisting the wires reduces loop area (and positive to the left, negative to the right for one twist cancels filed from negative to the left, positive to the right of next twist, at a distance.) Batteries themselves form a loop; if you were really trying to minimize radiated power, might arrange batteries so they also form a twisted loop.
For the most part, minimizing differential current is the job of inverter designer. Simply cable tying positive and negative together should be good, or twist if easy.
Different topic, those cable terminals are exposed and close. Make sure they can't come in contact. A piece of of insulation between them might be good.