[Accelo]

Tow away. I will tow just fine in stock form or properly rebuilt.
Yes you have a 4L60E in your Silverado.

GM renamed the 700R4 to 4L60's to keep the nomenclature consistency.
A THM is a 3L60. First number is the # gears, second is rear wheel drive and the last is the torque capacity.
The "E" on the end designates electronic controls.

I have a Silverado with 170K on it and have had to repair the transmission.
However, the center shell broke at the hub and this has noting to do with towing.
I do wish I knew the exact year of the transmission. 1982-1986 were not especially good transmissions. 1987 and up were excellent.
That said I would just tow and go. Doesn't sound like your load is a very heavy.
With lighter trailers, like an unloaded car trailer, I tow in OD.
GM has to make recommendations like everyone is an idiot.
Cheers