The answer to the second part that got my initially interested in this idea. After noticing what a certain combo was capable of, I was interested just how fast it could be in theory. Upon working it out I was quite struck by how quickly and easily it could win the game given perfect shuffles, and just how tight the solution was in some respects.
X = Copper or Estate
Open Silver/Bridge - shuffle 1 (B, S, 7*C, 3*E)
t3/4: BSCCC -> King's Court / CCCCE -> Bridge / next hand has EE - shuffle 2 (B*2, K, S, 7*C, 3*E)
t5: EEKBC -> King's Court
t6: BSXXX -> Bridge / next hand has XXXX - shuffle 3 (B*3, K*2, S, 7*C, 3*E)
t7: XXXXX -> nothing
t8: KKBBB -> buy 8 provinces
Kingdom cards needed: 2 (King's Court, Bridge)
Gained cards: 14 (1 Silver, 2 King's Court, 3 Bridge, 8 Provinces)
Shuffles: 3
Complexity: 84
I never actually calculated the exact complexity of my solution before, so I was somewhat surprised when it came in as better than chwhite's, whose solution I feel in some ways is "better", but the definition of the metric is somewhat arbitrary and by other measures a different one might have come out as "simpler". I personally am now of the opinion that the number of gained cards needs to be weighted less and the shuffles weighted more, each of which favors one of our solutions, but again, it would be somewhat arbitrary to decide just how to weight them and thus I just went with what was simple and had the required properties.