LS1 Swap 2000 Model Silverado 4L60E...will the trans hold up

Swapping an LS1 into my truck and debating on bolt ons cause I'm not sure the 4L60e could handle it in my truck. Using all the accessories, harness, intake, injectors(factory 4.8L injectors in my model are 3lbs larger than factory LS1 injectors), fuel rail and pcm from the current 4.8L which I had found metal chunks in its oil during a change. I have hp tuners so I'm remapping my fueling and timing parameters to factory LS1. Going to gut the stock cats on the truck y pipe. Debating on tuning it and adding any bolt ons because I am unsure of if the trans go towing shift kit will be enough to handle the LS1 in a full size truck. Any opinions on what to do would be helpful. I would like to not have to 4l80 swap the truck but if I have to I suppose I can. The LS1 has 60,000 miles and I'm buying it for a very cheap price.