First, OP was not connecting at LAX because he was on separate tickets. He was merely transferring between two entirely separate journeys which happened to end and begin at the same airport on the same day.

Second, US law is US law. MSC and IATA 302 are trade agreements which are called "rules" but have no legal application. Nonetheless, US law permits air carriers to use the MSC "rule" if the carriers wish. In this case, it doesn't matter.

Third, the US law expressly does not include any baggage waivers -- what OP incorrectly refers to as "excess allowances".

Thus, AS was free to interline the bags from ANC to SVO and onward to the undisclosed internal destination in Russia, but that has nothing to do with fees on separate tickets. The simplest solution here is that AS should not have checked the bags beyond the termination point of the ticket, e.g. LAX. OP should have collected the bags and checked them in with SU and paid whatever fees were due.

All of this matters with a departure from the US. If OP had a single ticket ANC-LAX-SVU-XXX, US law would have required the marketing carrier of the first segment, presumably AS, to provide on the e-ticket receipt, the baggage allowance for the first two bags on each segment of the ticket. That allowance would have shown the extra waiver for the AS segment and the standard fees, if any, for the remainder.