I actually have had success with a goofy deck I threw together abusing Persephone's power. I included Egrets and Adjusted Matrices as tools to use in the event I actually need to break the ice. MU is held in check with Net Chips (very flexible with big rig that includes Mopus, Equivocation, Hyperdriver) which synergizes perfectly with Kate's ability and the Tech Writers. Also running 3x Test Run/Scavenge combo to cheese out the Persephones. Rest of the econ is rounded out with Peace in our Times and Sure Gambles. Also packing Feedback Filter and Plascrete to survive kill.
Kate in the Underworld
Kate "Mac" McCaffrey: Digital Tinker
1x Deuces Wild ●
2x Employee Strike ●●
3x Levy AR Lab Access
3x Peace in Our Time ●●●
3x Sure Gamble
3x Test Run
3x Adjusted Matrix
2x Feedback Filter
2x Plascrete Carapace
3x Technical Writer
3x Persephone ●●●●● ●●●●
2x Magnum Opus
15 influence spent (max 15, available 0)
50 cards (min 45)
Cards up to Terminal Directive
Deck built on https://netrunnerdb.com.
In practice, when you hit those Barriers you frown hard because you can't let ETRs fire and expect to mill anything, even if they are Sentries at that point. But one lovely game, I ran R&D ice first turn, hit a Veritas and then slowly set up the rest of the game until I could get 2 Persephones out and start milling.
While the obvious play around is for the Corp to install over Sentries or to not rez them, if you time it right, you can hurt them a lot before they can counterplay, esp. if they are trying to rush out, which my opponent was. Final turn, I milled 18 cards with Persephone while using Equivocation to force draw other cards, resulting in a sudden mill victory when the Corp was on game point.
Obviously not every game will go this way (I've had some grueling matchups where the card does nothing) but since it's pretty unexpected, there's a chance for some mild success.
Let me know what you think if you give this a test run!