I imagine that would be very difficult to do, if even possible, its likely Murray was given specific instructions for the assembly etc. 1983 Sierras were a one year model that possible initiated in July or August of 1982 (maybe frames were even made before, since except for the fork they were basically a Sidewinder. I have a September 1982 (JT) bike and frame-wise the only difference from my April 83 (DU, August 27 build (Chicago plant no. 2?)) is the addition of an extra chainstay rear derailleur guide. The JT bike has an assemble date of April 7 1983, so its parts of the last batch moved from factory 4 to factory 1 before they closed. The JT bike seems to be completely original except the saddle. You may be aware of this timeline but, according to the USA trade commission in September 82 Schwinn's frame making plant #4 closed, and to some part that activity moved to assembly plant #1 that closed in June 1982, but even after then some activity moved to component manufacturing plant #2. Does anyone knows the closing date of plant no. 2? I hear late 1983, if we learn this date then we would know what the last Chicago assembled bikes are.
Likely, all frames made until late June (date code FU) were assembled by Chicago, and perhaps it's safe to assume frames GU (and HU if made) for the Sierra builds were possibly assembled by Murray, although is not clear if there was a back and forth movement of bikes to be assembled by Chicago.
I notice the OP bike has 1984 tires Panaracer?, perhaps he wants to share both stamps and pictures of the welds if it belongs to the mysterious fabrication period. Schwinn Sierra bikes from that/those last months is/are still USA-made bike/s with quite an special history.