I had several done in the mid 70s by a gentleman in Delaware who re-lined barrels and re-chambered your cylinder--you just sent him the parts. They worked well--no problems--and were stolen in a burglary several years later. One gun was a model 27 with a factory 44 target barrel, a clone of a model 24, and one of the most elegant guns I ever owned, fitted and re-chambered by Nu-Line Guns in St Louis MO. (I didn't buy any of the mid 80s issue of the 24/624, but supposedly there will be a run of them in the near future. I think at least one is in my future.)
I would contact Jim Stroh at Alpha Precision, a true gentleman and an artist. He does work that will make you proud.
If you complete this project, you'll have a unique and useful item. DON'T GET CRAZY WITH THE RELOADS and it will be more than adequate for anything a reasonable person will use a handgun for. If you have to max it out, get a model 29 or a bigger caliber! The only reason I use 44 magnum brass is because of leading/carbon ring issues in magnum chambers. I could very happily go through life with every 44 I own as a 44 Special, but that's not what you buy across the counter. You might do some checking on Ruger Old Model 357s converted to 44 Specials--these have a cult-like following on various single action forums. Those gentlemen are not shy about reaching for their wallets and doing some serious custom work!