Uh, yeah. That's not the way that I would have done it. Might be okay, though.
How far did you say the old axle slides into the new sleeve, and was it a sloppy or snug fit before welding? Is the 2 inch sleeve tubing (2 inch od x .25 wall thickness) or 1-1/2 nominal pipe (1.90 od x .145 wall)? If pipe, then the id is more like 1-5/8 inch and there is wiggle room (

not preferred, IMO).
Are there any plug welds inboard of the springs or is it just welded around where the two slip together?
You show the 8 inch measurement from about the middle of the drop forging. I'm not sure where Dexter's backspacing spec's are in reference to, but I suspect it is at the brake flange or wheel hub face. (Although some of the smaller numbers they list seem like it would not be possible if referencing the hub face, so...

)
8 inches doesn't scare me too much.
The axle is already installed/in service? If so I think the thing to do is test it out with an empty camper first. Start by making a few short trips around the block, make sure to hit a few potholes or speed bumps (gentle) and inspect. Do it a little faster/longer and inspect again. Put some load on it and do it again; inspect. Eventually you will either see a problem developing, or you will gain confidence that the "fix" is sound for you application. Assuming that the workmanship and materials used are good, and that you don't overload like crazy, I doubt that it would fail dramatically (although if the weld cracks from fatigue you could loose an axle stub).
I'm not a lawyer and there is no way that I can offer you professional advice from a far, so you will have to decide for yourself (or get someone local to give you a second opinion). Translation: I would like to remain conservative on this one.