I would never tow a sizeable load in OD. Even if the TC stays locked.
There is information missing in common "car lore" about why we are supposed you avoid OD. It's not Just the TC and fluid heat and clutch wear from that shifting. It has to do with the OD gearing itself.
I take the time to write this about once a year....
In OD the final ratio for the WA580 is 0.83:1.0. the 580 is geared a bit more than most transmissions.... the 545RFE for example is 0.67:1. This means that the driven gear is effectively smaller than the driving gear--- and that smaller driven gear has a lot of force applied to its teeth, as all of that power is a) happening in higher torque/lower rpm b) limited number of teeth/surface area due to the affective size of the gear.
In a lower gear, yes there is indeed a smaller (relatively) gear driving a larger gear, however the forces are less because it is basically on the easier side of the gearing.
So in OD, all of that power is basically sent to a gear that is restricted in size. What happens? It heats up. It can become weaker via fatigue, and it heats the oil in the meshing surfaces more.
This was from a 4x4 mag decades ago. I don't recall which one, and they certainly explained it more elegantly than I can. However, I discovered what I think is verification of this in my Tundra once I put a scangauge on the trans temp. On level ground, with no shifting back and forth, and a significant tow load, the trans runs cooler when out of OD. It's a little difficult to detect unless you watch it in mine because at 180F the t-stat opens and engages the external cooler. But from what I can tell, this seems to hold true.
GRANTED, YMMV. Different trans are built differently. But as a general rule, it makes sense.
m