refacing a HS barrel in the lathe due to dry fire?

First topic message reminder :

Long time lurker, first time posting. 
I recently inherited a HS model 107 and started using it in local Bullseye matches, needed to add a mount for red dot but dont want to drill the barerel, love the gun and want to keep it the way my Grandfather left it. 
SO purchased a mint looking HS 107 from GunBroker to use as my bullseye Gun and find that the seller posted just the right pics to hide major dry fire damage to the barrel. Im looking for a chamber iron to try first but having doubts it will fix this damage. Does anyone have any experience machining one of these? Will it cause any issues Im not aware of? I dont think it will be much, maybe .015 thou but I dont know if that will be a problem with the ejector slot etc etc. I had been waiting on a few other purchases at the time and left this sit at my dealer too long to get any help fropm GB or the seller.  I will likely order another barrel from Dave at LSP but in the meantime I would like to make this usable for myself or resale etc etc. 
Thanks for any advice, I will be posting more in the future as this site has been an excellent source of info!

Hi Coupebuilder,
I've welded Hi Standard frames and slides, but not a barrel. Mdl 41 slide catch cutout too.
Used E70-S2 rod on them with no issues. Heat it up to around 250f and then weld it.
Betting the HS barrels are mild steel, so RG-60 or E70-S2 would work fine.
I recently welded a Hammerli 208 slide up by the forward spring seat. The shooter had an analysis done before which said it was 1215 high sulfur steel.
I used RG-60 on that and so far (fingers crossed) it has held up. Did a lot of sucking the sulfur out before welding it.
Hope this helps,
Wes

Thanks Wes, Im going to go with the chamber Iron first, then try the tig route I dont see it being overly complicated like some of these guys want with bushings etc etc..all of which would need the extractor slot reworked and are a lot more invasive.in the end its worth 200 bucks in good shape but can be replaced for 185 with a match barrel from LSP.  More just an annoyance I got stung on it and want to make it usable or saleable in the future.  In my mind its hard to imagine them making barrels from mild steel and not some alloy but in this case its not really a functional area that would matter in any way as far as accuracy. 
also...curious about the rg60 rod...isnt that a gas rod?  I use a ton of er70-s2 and s6 as well as Silicon Bronze but havent tried the rg 60 usually the HS steels and Lead like 12L  I stay away from just for liability reasons.

Clean the lump out with a finish match chamber reamer. Manson or Clymer