2009 Ford F350 6.4L Engine P2704 Code: Shifting Issues Only During Towing?

Hello! I own a 2009 Ford F350 with 167,000 miles. In January, I purchased a horse trailer and drove it for 9 hours to deliver it. On the way back, I began experiencing shifting problems — the truck refused to shift properly, and a connecting rod failed through the engine. This was the first time I ever had any transmission-related issues before this. After replacing the engine, the shop drained the transmission fluid and stated they didn’t believe it was damaged. Once the new engine was installed, the truck shifted normally again. However, after reattaching a trailer, I started noticing shifting problems again — specifically at the beginning of towing. During one recent trip, when I started hauling the trailer, the truck wouldn’t shift. I pulled over and accelerated from a stop; it shifted fine afterward, and no further issues occurred. The check engine light (wrench icon) came on during this incident. After running diagnostics, code P2704 appeared. I removed the trailer at home, turned off and restarted the truck — shifting worked perfectly, and the wrench light disappeared. I’ve been advised by a local shop that a new transmission is needed due to the P2704 code. However, I’m wondering: can a failing transmission cause intermittent shifting issues only when towing? Does it typically show symptoms like this — normal operation when not hauling, but failure at startup under load? Thanks for any insights or experiences with this specific fault code on the 2009 F350 6.4L engine!