Newbie tire fitment questions. Help!

[WBusa]

Here's the deal: we bought an old (but basically sound) small two-horse, twin axle ball-hitch horse trailer, model and year unknown. We've been towing it (in light service) for a year now. Just today I read the tire sidewalls, and my hair stood on end. My first problem is, they are garbage tires...no-name "made in China" with no DOT label, so they must be pretty old. They're P215/75-R15s. OK, so my second problem is these are passenger tires, which I now understand is a no-no.

With my confidence in these tires now thoroughly shattered, I measured the outside visible rim diameter of the wheels, which is 16 1/4"...so I'm assuming these are 15" wheels, since the visible rim diameter of my Ram (which I know is a 16" wheel) is 17 1/4".

Last but not least, it appears that none of the major tire manufacturers make an ST215/75-15 (well, there's a Badyear Wrangler HT in that size, but I don't want it). Now, I don't actually know that these are the right size tires for this trailer in the first place (no owner's manual, no sticker). In fact, considering they're passenger tires I figger there's a high probability that everything else about them is wrong, too.

So my two questions to y'all are these:
1. Measuring the wheels as I did (i.e., to the visible edges, with a tire mounted), am I pretty safe in assuming these are in fact 15" wheels?
2. If I can't find LT215/75-15s, how much latitude do I have in playing around with the first two numbers? For example, Cooper (I love "Made in USA"!) makes a LT235/75R15 in its SRM II Radial LT. If I made sure it doesn't rub the fender, the wheel well, or its companion on the other axle, could I substitute this size for the existing 215/75s? Or are their additional considerations involved besides just clearance? (I have a feeling this is a really dumb question...like I said, I'm a newbie when it comes to trailers).

I really wanna get this right, because horses all over the highway is really bad news. Thanks for your help!