I just still have trouble justifying Muto on the basis of the impermanence inherent to Muto magic. If pressed (as I apparently am) to provide a logical alternative, I would then add either the Ig req or an extra ReIg effect to simply melt the iron ends together before applying the ReTe finishing process.
Same result by different, and more plausible hermetic means IMHO. To each their own 
for this you dont want the muto to be permanent, you temporarily soften the metal so it's like clay, then mundanly squish it together, the muto effect ends. but the crafting done non magically remains.
Whether I would want any Muto effect to be permanent or not really isn't the key issue (especially since Muto NEVER can be permanent no matter what one wants).
As I said, it's a matter of "to each their own" as to means. I simply do not consider any aspect of this requested methodology as involving Muto in any way, shape or form. since one is not changing the the essential nature of Iron to any other material substance., Softening iron. to my mind, is purely a Rego effect or at the very extreme an Ignem requisite within (or linked to) a Rego effect. I would never rule any involvement for Muto, but thats me.
Whatever works for others is fine for them and for the system itself as I understand it. Vive la difference! 
So Rock of Viscid Clay isn't used in your games, I take it?
Hasn't been used et as far as I can remember but touche for the reference .
I shall give this a rethink 