Baseline AMRAAM? The AIM-120A that's been out of production for almost 15 years? AIM-120C-7 is about even with the R-77 and the AIM-120D comfortably exceeds it in terms of range, and massively exceeds it in terms of seeker technology. 80km if it's lucky- SH has a fraction of the RCS of the Su-27 series. You're probably looking at detection ranges in the >150 nm range for SH's finding Suhkois. Even so, the APG-79 is LPI, so no matter what the SH is going to get first look by a comfortably margin and be able to dictate to a large degree where and when the engagement starts.
Thinking the game stops once missiles are launched is very simplistic. Most Russian missiles are still operating on older technology R-77 is no exception thanks to the post-Cold War defense meltdown while AMRAAMs have been constantly updated. BVR is highly dependent on ECM, something which the US has had a reasonable advantage in for a very long time. Low RCS Super Hornets with towed decoys and comprehensive EW suites they are going to be extremely hard to get a useful lock on. Once they get Growler support and AESA jamming modes, it's going to be even more difficult. Add in even harder to find F-35C's and you have a suicide zone for any Flanker variant around any US carrier.
Basically, you're going to see the high-performance Flankers' performance advantages evaporate when faced with a huge situation awareness problem. It's hard to dodge anything when you don't know who the shooters are, where they are, or when they launched their missiles. Once again, even if the Flankers manage magically to get through, at best they're going to get an even loss ratio thanks to High-off boresight missiles.
Bet my money on SH anytime anywhere.
Cheers,