Rong, from things you have said earlier I have the impression that you have access to a lathe. That means you just need a chunk of cast iron, to make a new pulley. The world is full of cast iron junk, and any bit that is bigger than your pulley in all three dimensions will do. Personally I tend to like cast iron because it machines so nicely. Yes, you do have to wear eye protection when you are turning it, but really you should anyway, so it just encourages that good habit.

The Honda G65 is an old engine, though not as old as your Briggs, and is not rare. My suggestion is that you initiate a very low intensity search for one, and meanwhile happily use the Briggs. When you find a Honda in the right condition at the right price you make the changeover. It looks as if it will involve no more than two new belts and perhaps a minor correction of the clutch operating lever.

How you go about restoring things is a personal preference. My preference is to spend very little money. In your current situation I think I would be making a new clutch pulley because that is easier than welding the one you have, or even searching for a second-hand one. I would regard the modified rear wheel and axle as a low priority problem as long as it works properly as-is, so I'd be watching for a second-hand wheel, but not worrying about it in the meantime. Incidentally, I think shipping a second-hand wheel from Australia need not be expensive if you shop around and are satisfied to ship it slowly rather than quickly. The axle shaft is awkward to ship, so I might not do it, I'd examine the feasibility of making one from a piece of bar. However I prefer "real" parts to imitations, so I'd be contacting people in Australia who have junk-class HD8s and seeing if we could do business regarding a selection of parts.

To me, expensive restoration is no fun. I derive my fun from finding cheap solutions. We have many members at Outdoorking who feel differently, and are happy to pay as much as they can afford for a perfect job achieved quickly. Both approaches seem legitimate to me, but I happen to be a cheapskate.

Note that I would not contemplate making a wheel, because that (by my standards) is way too hard to do.