OK, let's think about this logically.
There are five (5) TRS circuits. One of those (the T41 circuit) goes directly from the TRS to the PCM; the others go to the TCM. I'm guessing that the T41 circuit is the "neutral safety" signal, that would be grounded (I'm guessing) in Park or Neutral. The P0706 fault means the TCM saw an "invalid" TRS code, that is, a combination of switch states (on its four circuits) that should never exist (that doesn't correspond to any valid gear position). When the TRS code is invalid, the TCM calls for the PRNDL display to be either blank (nothing highlighted) or "all" (meaning ALL the PRNDL positions are highlighted). I'm not sure which one ("blank" or "all") the Aisin trans uses. The P0850 fault means the PCM received a CAN bus message showing trans in Park (when vehicle was actually moving at greater than some threshold speed), or trans in Drive while the engine was being cranked. So P0850 relates only to a CAN bus message (not the state of the T41 circuit that the PCM is monitoring). The CAN bus message for trans PRNDL position must originate from the TCM.
• So the P0850 fault could be set if you throw the trans into Park while driving down the road, but that would not set a P0706 (or blank out / light up all the PRNDL positions). And I'm assuming you didn't actually shift it to Park while moving.
• A bad TRS (or bad wire) that caused an invalid PRNDL code (and P0706 fault) should not cause a P0850 fault, since it would not cause the TCM to send a CAN bus message for Park or Drive (at an inappropriate time).
• If the T41 circuit is the "neutral safety" circuit, then it would be possible (if T41 were grounded all the time, let's say) to set the P0850 fault, if you actually did crank the engine while the shifter was in Drive. But again, that would not set a P0706 fault, and I'm assuming you didn't actually do that.
• Since P0850 requires a VALID TRS code (so the TCM is communicating either Park or Drive over the CAN bus), while P0706 requires an INVALID TRS code, I don't think both codes can be set simultaneously. But apparently your problem is causing an invalid TRS code (and hence, P0706) at some times, and an incorrect Park (or Drive) indication (and hence, P0850) at other times.
• Let's call the four TRS circuits that connect to the TCM A, B, C, and D. (In actuality, A is the T42 circuit, B is the T3 circuit, C is the T1 circuit, and D is the T4 circuit). In Park, A and D are "active" (which I'll assume means they are grounded). In Drive, B and C are active. So I don't think there's any single circuit failure that would give you a false "Park" reading while you were driving down the road. However, Neutral has B and D active, and in the transition zone between Neutral and Drive, B, C, and D are all active.
• So I'm wondering if perhaps your C circuit is "active" (grounded?) when it shouldn't be. If C is active in Park or Reverse, that would give you an invalid TRS code (and thus, P0706). If C is active in Neutral, the TCM will think the shifter is in between Neutral and Drive. I'm guessing that the TCM might send a CAN message for "Drive" in this case (if the TCM thinks the shifter is in between N and D, it is safer to tell you it's in D, than to display N when you might actually be engaging Drive). So, if the shifter is actually in Neutral, the T41 circuit would tell the PCM that it's OK to crank. But the TCM will be seeing "transition zone between N and D", and may therefore be broadcasting "Drive" over the CAN bus. If so (and you start the engine in Neutral), that would explain the P0850 fault. So, do you ever start your engine in Neutral (rather than in Park)? When you get the "all yellow" PRNDL display, is that when you're in Park or Reverse? If you shift back to Neutral or Drive, does the PRNDL display then read properly? That would support the "bad C circuit" theory.
As you can see, there's a whole lot of "guessing" on my part here. But I think this offers one feasible explanation. The "C" TRS circuit is known as the T1 circuit in wiring diagrams, and goes from pin 1 on the TRS to pin 10 on the TCM. It also goes through a wiring connector behind one of the front wheelwells (at pin 16). The problem could be a bad TRS itself, or could be a wiring problem (bad connection, corrosion, etc.). I would check the wiring connections over visually (especially the connector behind the wheelwell) before replacing the TRS.