I appreciate all of the feedback! The clear overall census is that the best route would be finding someone who could shorten the horizontal beam of the existing tire mount and re-welding it back into position.
I am still entertaining other viable options. Perhaps making the modification to the existing mount would be the least problematic. If this ends up being the solution I will bring up a side issue likely to be encountered specific to this specific make of trailer.
The reason I am entertaining other options is purely from the stand point of thinking how much space that could be saved for carrying items to bring along for camping. Once I considered this I have been reluctant to give up on it.
I've further checked into the vertical wall mount. The company that makes this does install tires on the exterior sidewall of their teardrop trailers. I asked the question as to whether the little guy would be able to support the extra weight. He wasn't sure whether the wall of the little guy would or wouldn't support the weight as compared to their own trailers. There is a small interior bracket that they also sell to strengthen the attachment. From looking online it appears the wall of my trailer would include 5/8 inch birch plywood covered by 1/4 composite material covered by the outer shell. Without a clear reference to the viability of this and not wanting to gut my trailer to make it stronger I believe I'm going to have to shelf this idea.
This morning I found another idea. Prior to this I have abandoned the idea of mounting my tire to the side of the trailer tongue as it would interfere with my tongue box and henceforth just not fit. Then I saw a picture that shows the tire spanning the tongue box.
To be honest I have no idea in how this could be attached like this with a standard tire mount. I've also noted that the tongue box was shifted away from the tire side to allow clearance.
In looking at my own setup I can see 1 conceivable way of doing something similar with the materials that I already have on hand. First of all the spare tire mount is fixed to the 2" square tubing by straddling the tubing and being bolted down. The below picture "may" show the straddle, and the fact that at least a narrow 5 inch groove was necessary to get past the internal grating in the tongue area.
If I were to angle grind a narrow channel similar to the one already existing along the tubing just behind my tongue box I could move the tire mount to where the spare tire would fasten overlapping the outside of the tongue box favoring to the back side of it. This potentially would remove my issue of tire clearance with just grinding out a narrow 5 inch groove.
The biggest detriment to this that I see is that there would be a load imbalance. My counter to this issue would be that my portable but cumbersome Coleman grill would be held down on the other side. Whether this would be enough I don't know.
Would this be viable?
Oh; by the way I live in northern lower Michigan.