The past couple of days I tried a nodal analysis approach in comparison with the previous loop analysis approach. I didn't find much improvement in the speed of simulation. However, the matrices are much more unstable and the simulation time step needs to be much smaller. There probably are improvements I could have made to reduce this instability, but I would rather go with the loop analysis method.
To speed up the simulations with loop analysis, the only method I can think of is to maintain a logbook of all the changes taking place in the circuit and how this impacts the loops. This is under the assumption that there will be a finite number of changes possible and therefore a lookup table can be used to get rid of all the loop manipulations. So the simulation will be slow in the beginning but will speed up later.
Anyway, I am taking a break for the next four days to hang out with friends who are beginning to wonder if I am still alive. Seasons greetings to those who celebrate Christmas and for those who don't (and that includes me) get drunk and be merry anyway. See you before new year when I hope I will release my next version.