The best option is to find 3 other buddies each with 3 of their own machines. Then you take turns hosting so you get 4 rounds of kills. Even at master 1, you should be lucky enough to get at least one part from each pair of bosses.
If you insist on save scumming then why not just use one machine and kill the bosses. No piece, reload until you finally get it. Then save and use another machine until you get the right portal and get the drops. Save and use the 3rd until you get the right portal and get the drops... That's exceedingly boring though just for a single hellfire ring.
Just do what most people do, turn your normal gear farming run into a key run as well. Make the keywarden a standard part of any farming run because they can also drop other legendary's anyways. The absolute best way is to do these key runs with 3 other people. You're all getting keys at the same time and will all be able to build 3 machines together. Absolutely no more efficient way to go about it than this. You do 4x the work in the same time it would take you to do it solo, plus you get the bonus exp and magic find.
Dark Souls Youtube channel - Tutorials, challenge runs, pvp and new content. http://www.youtube.com/user/vageta311