I am embarking on this exercise shortly.
The "welding technique" commonly referenced is done in a couple of different ways.
One way, possibly the easiest way, is to weld the shackle bushings. You grind out the thin or worn portion cutting it back into the more solid material. Then you place and hold the bushing in place with baling wire as far "into" the solid eye as you can get it. Then you weld up and rebuild thickness using the shackle bushing as your "backing."
The downside of this method is you leave it so that once you wear through the bushing you have to do the whole show all over again - you've lost the advantage of bushings you can drive out with a punch as they become integral to the axle housing.
However, for anyone conversant in welding this is not a large downside: its always possible to do the same repair a second or even a third time. Those of welding experience have no fear of "remaking" anything welded - its only "time" and not even that much cost in grinding or weld electrode.
A more true to original methodology uses either carbon (graphite) or copper slugs to replace the bushings: you weld up around the slug by MIG or TIG or even stick (if you're good.) The copper or carbon are then removed by physical means which may mean machining in the case of the copper, or by merely "breaking it out" in the case of carbon.
Copper if kept "cold" will conduct heat away from the weld. It is possible to "burn through the copper" if you weld too vigorously in one spot so some "artfulness" is required with copper. Running water through a copper pipe is an excellent way to remove heat and prevent burn-through.
Carbon (graphite) likewise does not burn but "embrittles" under heat, aiding removal - this is commonly done with a punch and ice-pick. Graphite has a melt point about 5000F. Reports online indicate that graphite "cylinders" are available for EXACTLY this purpose in varying diameters and available on Ebay in 3/4" size - the same as the exterior of the shackle bushings.
I was headed to brass slugs bored out which I would drill through and provide water flow with Tygon tubing - but I have read a bit online and now feel confident enough to try the graphite method. Its use is VERY common in industry and even includes "threaded" graphite cylinders where one can "weld" a threaded hole even.
I am fortunate to have at least three pairs of trumpets to experiment with.
Joe K