I am not seeing how the request system is vulnerable. As I understand it there is a register of absentee voters, ballots are generated (sometimes with privacy sleeves/envelopes etc) and printed with barcodes that tie ballots back to a specific voter ID up until the point that information is separated for counting.

Given knowledge of how that system works and controls put around it I doubt any such vulnerabilities could exist that could be found by statistical analysis that isn't already being done...

I also think you missed the point of my last sentence which is that you could consider the actual ballot system a lot like AES or any other cryto system you might be familiar with.

Cracking the crypto system is stupidly hard because a ton of time was invested making that so. Instead attacking the stuff -around- the crypto system is likely to prove much more fruitful. i.e social engineering, side channel attacks

In the same way the attacks I listed above elicit the desired effect (a certain candidate having an unfair advantage) but without attacking the actual ballot system itself (which is likely far too difficult).

Essentially it's a case of lower hanging fruit, you don't need voter fraud to "steal" an election.