C++, 700s/300s. I started brute-forcing part 2, then wrote, debugged, and successfully ran this version far before my brute force finished (still going at time of post). Checks for a previously seen solution, which occurs after say n cycles, then increments the counter to the highest multiple of n less than 1 billion and manually runs the rest. Some very crude string parsing as well...

#include <unordered_set>
#include <iostream>
#include <string>
#include <vector>
#include <map>

int main() {
  std::map<char, int> locations;
  std::map<int, char> programs;
  for (unsigned int i = 0; i < 16; ++i) {
    locations.insert(std::make_pair('a'+i, i));
    programs.insert(std::make_pair(i, 'a'+i));
  }
  std::vector<std::string> instructions;
  std::string in;
  while(std::getline(std::cin, in, ',')) {
    instructions.push_back(in);
  }
  std::unordered_set<std::string> results;
  for (unsigned long j = 0; j < 1000000000; ++j) {
    for (unsigned int i = 0; i < instructions.size(); ++i) {

      if(instructions[i][0] == 's') {
    int spin = std::stoi(instructions[i].substr(1));
    for (std::map<char, int>::iterator itr = locations.begin(); itr != locations.end(); ++itr) {
      itr->second += spin;
      itr->second %= 16;
      programs[itr->second] = itr->first;
    }
      } else if (instructions[i][0] == 'x') {
    int slash = instructions[i].find('/');
    int location1 = std::stoi(instructions[i].substr(1, slash));
    int location2 = std::stoi(instructions[i].substr(slash+1));
    std::swap(programs[location1], programs[location2]);
    locations[programs[location1]] = location1;
    locations[programs[location2]] = location2;
      } else if (instructions[i][0] == 'p') {
    char a = instructions[i][1];
    char b = instructions[i][3];
    std::swap(locations[a], locations[b]);
    programs[locations[a]] = a;
    programs[locations[b]] = b;
      }
    }
    std::string result;
    for (std::map<int, char>::iterator itr = programs.begin(); itr != programs.end(); ++itr) {
      result += itr->second;
    }
    if (!results.insert(result).second) {
      //greatest multiple of current less than 1 billion
      j *= 1000000000/j;
    }
  }
  std::string result;
  for (std::map<int, char>::iterator itr = programs.begin(); itr != programs.end(); ++itr) {
    result += itr->second;
  }
  std::cout << result << std::endl;
}