To answer some of your questions: no oil cooler installed. Transmission was serviced about 20k ago which did make the transmission smoother at the time. Rebuild cost is $4800 which includes a new torque converter
I hate GM/H and their dealers for not being very clear about the transmission service requirements.
Not sure about the 6l45E but the 6L80E has a fluid change interval of 150,000kms under normal driving conditions... GM/H says that one should use a 75,000km change interval under severe driving conditions (city stop/start, towing, hot climate, etc). And many forum members feel that even GM's severe schedule is a long time between drinks and one should change trans fluid at 50,000kms
Really, for most who live in cities with stop/start traffic and considering our hot climate, you'd think the trans service interval should be at the severe end of the schedule, or sooner, yet dealers are moot on the subject.
This is even more so if you tow where an extra trans cooler would be a good investment in preserving your transmission. But sadly, if you don't know these things, you don't know and can get caught out by GM/H's games at creating service intervals that show reduced running costs for those that only keep their cars for 3 or so years. The rest of us get shafted by these fairy tails called service intervals...
Unfortunately I'd say 135,000 km trans service is a long time between drinks and as a result some may end up with a rebuild rather than the cost of a few more trans services as a result
So what can you do? Install an extra trans cooler in line with the factory cooler if you tow and change trans fluid (and filter?) every 50,000kms (as fluid changes are much cheaper than expensive rebuilds). Also change engine oil and filter every 7,500 kms and diff fluid more regularly than GM/H specifies. If you have the interest and aptitude, learning to do it yourself can help reduce the extra service costs but even this isn't a guarantee against hardware failure because shite can still happen. And it happens more often if the product has some shortcomings within/by it's design.
The following video may also be interesting as it highlights some potential poor rebuild issues with 6LxxE transmissions that in this case may have caused loss of reverse.
Not blaming you or being negative, just telling it as i see it with the limited info posted.
Shite happens and hopefully you'll be on your way and the rebuilt trans will reliable for years to come.
Me, i'd want the trans shop to put all the old parts in a box so i can look at them and/or have them as paperweight for my desk/office... I always ask for such to be done... but that's just me