I've used those same tires - Kenda Loadmaster K550's on our boat trailer with good success. No unexpected issues other than a cut sidewall when I ran over some unavoidable debris on the road. Their source changed from Taiwan to China at some point, but again, no issues.
I've gone to a rotation, and I'll allow my oldest tire to be up to 9 years old. It is always the spare - I put my newest tire on, and take the oldest one and move it to the spare location. The spare gets replaced to become the new tire in the rotation.
I don't know how much towing you do, but at 15 years old, they've served their purpose. And traveling without a spare, I'd say lucky too...
Various outlets will give different opinions on tire time replacements. I think it all comes back to the usage and storage of the tire, as well as the climate. I'm not in Arizona, I don't store the tires outside in the sun for the year, and I don't put on more than 500 miles or so a year. YMMV...
If you want the same tires, they are available at decent prices from an e-retailer for trailers and leave it at that. PM me if you need the actual name from there...