After playing with this card for a little bit, I can confirm that attempts to make Slee's Pachinko Parlour with cheap ICE that the runner normally doesn't have to break are largely doomed to failure. She just doesn't cost enough to trash to protect herself, and if you try to run her out of faction in CtM or Industrial Genomics to rattlesnake people away from trashing her you'll run right out of influence to do anything else.
Yes, you can protect her in what would be your scoring remote. Yes you can make someone pay 5 to get past a free to rez Bandwidth to get to your HQ safely, but that's exactly what they'll do if you turtle behind porous ice without a place to advance agendas, and Slee will stay sad at 1-2 power counters until a Political Operative comes to take her out of her misery. She just isn't quick or dependable enough to build a kill strategy around. If she ever becomes threatening enough, they'll come kill her after they've amassed the credits to do it properly, Prisecs be damned. And you'll be stuck trying to sneak out agendas on a secondary remote while your centrals are spread thin.
However, that all being said: I believe she's still marginally useful. More than some give her credit for.
The best use of this card to me seems not to build a deck around (though you will be sorely tempted to), but rather as a way to threaten the runner's sense of security in facechecking ice until she is dealt with properly as a way to buy time to set up a proper Glacier. Throw her out in her own remote with a Prisec or a Mumbad Virtual Tour. When the runner feels pressured enough that they no longer feel safe facechecking new ice on your centrals, they'll come to trash her and give you a small scoring window to work with. Sometimes, that's all you need. Aim not to ever kill them with Slee, but instead to put a mandatory break period for the runner somewhere 3-4 turns out.
There were a few, brief, shining moments in my head the first time I read Slee where I thought I could Dedication Ceremony a Mumbad Construction Co. straight into Slee. But sadly 'tis not to be. If for some reason there are ever just one or two more cards that are willing to spread a power token or two put this card back on your radar though.
As of now she's not good. But at least in concept she's fun.