When Exile came out, I really wanted him to work, but he didn’t. With any decent deck you had to ask yourself, ‘why wouldn’t this be better in Kate?’.
I’m not sure this deck really answers that question, although I can see that it tries.
Kate’s ability (-1 cost on first hardware/program install) is generally better than Exile’s draw a card when installing from the heap, largely because ‘installing programs from the heap’ is a smaller subset of ‘installing hardware & programs’. There are only two occasions where Exile’s ability is better.
The first occasion is when you are installing 0 cost programs from the heap. At zero cost, Kate’s ability is wasted. The only 0 cost programs I see here are SMC, and Harbinger (which I suspect you will rarely install from the heap). I’m not sure that’s enough.
Edit: I see Scheherazade in there too, so I guess that’s a little better.
If you want to strengthen this aspect of the build, take a look at some of the 0 cost programs that you might reasonably install from the heap. Faerie is an obvious one, and Endless Hunger actually plays really well with the assets you are planning to install for Aesops, so it could be a great trick to include.
What about Inti for Ice Wall and Wraparound?
Retrieval Run plays very well with Exile, of course, and because you pay no costs Kate gets no added value while Exile does. Very nice with Femme, if they have not been icing Archives.
The second occasion where Exile’s ability is better than Kate’s, of course, is if you are installing multiple programs from the heap in a single turn. That’s going to be a play decision, of course, and very much dependent on player skill.