Randomness is not a problem. Again, juries are selected at random, and in groups of far smaller people.
The point of selecting them at random is it again limits the influence of outside forces. Before the selection is made, it is impossible to target anyone to try and influence their vote. The only opportunity to make an attempt is in the brief period between the selection process and the electors actually assembling.
I’m sure most Democrats would just vote for whoever the party tells them to. However, the process of voting I’ve designed for electors creates strategic incentives not to just follow along. There are five nominees, and they’re voted on successively in pairwise matches. It would be very easy to pick an alternative some Democrats would like better than the DNC endorsement.
In fact, let’s consider a scenario where a majority of electors were Democrats. How do Republican electors respond? Well, the rational response is to recognize the winner will be a Democrat, and so strategically nominate moderate Democrats who are willing to talk with Republicans. While this might not appeal to most Democrats, it will appeal to some. And Republicans will certainly prefer such a result over the alternative.
And I’d stress that the moderate Democrats who accept the Republican compromise have really good plausible deniability: In the final head-to-head vote between two Democrats, how do you distinguish which Democrats didn’t cooperate? The answer is you can’t. They’re all Democrats, and they’re all voting on Democrat candidates. If the DNC wants to start a witch hunt on their own membership, they are bound to make lots of false positives. That simply isn’t worth the effort with 270+ people.