OK, some basic points:
1. "China Bomb" is not the same as "made in a Chinese factory". China has some brands or factories with low quality standards, but they have quality production too. When an internationally known brand has tires made in a Chinese factory, they still meet the company's quality standards. There are many quality tires still made in the USA, and also in Korea, Japan, Europe, etc.
2. LT tires can carry less weight than an ST of the same size, but if you replace your LT tires with any brand of LT of the same size, the load rating will be about the same. The key question is whether the original tires had enough load capacity (max load rating) to carry your trailer safely and with some extra margin of safety.
3. Michelin tires are notorious for weather checking, tiny surface cracks. Disconcerting, but not necessarily dangerous. Other brands use different rubber compounds and not as likely to show surface cracks, but not necessarily ant better tire. I say this, even though I'm NOT a Micheline fan!
The trailer tires have to carry the max weight on the axles, which generally is 80% of the trailer GVWR on a 5W. If 19,000 lbs is the trailer GVWR, than 80% = 15,200 lbs. Spread on 2 axles (4 tires) that is 3800 lbs/tires, WAY over the load rating for those 235/85R16's you have. If its a triple axle trailer (6 tires), than it's OK. So first you need to determine what load the tires carry and what size or load range is adequate for the task.
Assuming the size an LT type is OK, there are plenty of quality brands in that size. Firestone and Goodrich (a Micheline subsidiary) make it, also Cooper (USA), Hankook (a top Korean mfgr). Yokohoma (Japan), and General (USA).