I can’t help but think you should have Federal oversight of elections to offices at least at State Congress level and above, in the UK we have the Electoral Commission which has wide ranging powers and can bring evidence to criminal prosecutions.
Such prosecutions are handled by the Crown Prosection Service, and obviously there are various sanctions available.
The critical question is who controls the CPS and the Electoral Commission - neither are partisan political appointees although they are formally apporved by the House of Commons - but it is a bi-partisan process and seems to be far more a final seal of approval following an open competition application process, it would be highly unusual for anyone to be rejected following successful application.
This would also need to have an independent Boundary Commission - again these are not partisan appointments.
The UK electoral Commission not only deals with political elections for national and local government but also for matters where national organisations have elections such as trade unions and internal political party elections, and those organisations must pay for this involvement. They also become involved in supervising the running of those elections, ensuring that the various requirements are being met, although they do not do the count itself of run the polling stations or the other physical parts of the election.
I understand the scale of operation in UK elections is a much different one to that in the US, however you do have pan-national law enforcement by various agencies, I cannot see how taking oversight away from states and Electoral Boundaries taken into a Federal Agency