Laws can be passed dictating that FEC must always have a quorum, and that if positions are unfilled by the President for X amount of time, Congress gets to nominate someone.
Laws can also be passed giving the FEC far sharper teeth in terms of investigative and enforcement power. Maybe have an FBI white collar crime task force assigned specifically to election security and fraud - given federal elections from 2016 to now, it's clearly warranted.
The nomination rules could also be changed, perhaps have the President nominate individuals well in advance, for positions they wouldn't fill until after the next general election, to prevent nominating people with the intent that they find in your favor when you are campaigning for reelection.