I'll throw a whole new suggestion at you.
Go to SARCO and look up 1903 Springfield parts kits.Then look up Criterion 1903 replacement barrels.
You see,there are not many Springfields available out there and you can make yourself a fine specimen of a 1903 Springfield.This rifle is a ticket to shoot in CMP vintage rifle matches.Ypur 1903 has far more value as restored to milspec than it does as a make-do 7x57.
Now,I understand you want a 7x57,cool! Great cartridge!I think if you look around SARCO,J+G,Springfield Sports,etc you can find any number of 98 Mausers actions for a reasonable price.Then you may easily screw your Mauser 7x57 barrel into a 98 Mauser Action.There are more stocks and parts available for Mausers and you will end up with a very nice rifle.
If you have no interest in restoring the 1903,I suspect several folks here may make you some inquiries,and if you make a post in curios and relics,I'm sure you will get support for the idea of restoring the 1903 action.
As far as your ideas on thread conversions,IMO,for safety sake,this is one place you just do not improvise.If you are going to build a rifle,barrel threading,chambering,and headspacing need to be right,period.
Have fun,keep us posted.