Before you go through all the trouble of jacking a tire off the ground - have you tried rolling one tire up a ramp and eliminate the jack issue altogether?
That is easy enough to test the next time you move the trailer. If it works for your configuration go and buy one of those "ride on jacks". Not the one you roll the axle onto, rather the one you run the good tire up on.
The wheel rated at 3400 pounds holding up 5000 pounds is not an issue, you are stopped and have no dynamic loads on the wheel.
Besides, if you have a flat you already have a dynamic load on the good wheel while trying to get off the road.
My trailer sat on frame jacks for 30 hours at Mor/Ryde with no problem.
I see no reason why you can't jack on the frame. The problem is the distance from the ground to the frame.
Personally, I would use a 12 ton bottle jack, and a low profile one at that. and block it up to get as close to the frame as you can before extending the piston.
BLOCKING THE JACK
This is the critical part. Use multiple pieces of wood and criss cross the pieces as you go up. See the attached PDF for an example.
We have picked up tens of thousands of pounds this way.
You don't have to get as fancy as the PDF shows, we tend to overdo everything
For us, I would think 2x6 boards about 12" long would work fine. You probably already have some of your cribbing in your landing gear blocks bin.
A block of wood between the jack pad and the frame too. Unless you have a friend make you up a "jack" cradle (U-shaped piece of steel to cradle the frame with a piece of pipe welded to the center).
You all would be best off, if you have the inclination to do this, to try it on a level area when you are having a "good" day.
Do it once having a cup a coffee and you will be able to do it when you "have" to change a tire.
Either way I wouldn't change a left side tire on the highway, unless my brothers in the big red trucks were "lane blocking" for me.