I would just keep on using the inorganic fertilizer, and supplement your soil with some organic amendments. It's going to get complicated to alternate one then the other, I think. You could do more harm than good if you over-fertilize, both to the soil and to the plants.
As long as you flush the salts out of your pots occasionally, (a really thorough rinse with the hose, or a heavy rain does it) and don't exceed the recommended amounts of the inorganic fert, I think as Sally said it's pretty much all the same stuff once your plant gets to absorbing it. Don't forget that in winter your plants will slow down or even go dormant so you need to adjust - i.e. reduce - the amount of fertilizer they get to account for this. If a plant's not growing it doesn't need fert.
You can get bagged compost which is great, and I've been using alfalfa pellets (horse food) to revive tired soil in all my pots of plants and Earth Boxes lately. It is a wonderful amendment as far as building the micro-organisms in the soil. A small handful in a gallon size pot, up to a few cups mixed into the soil in a big pot. Spring and fall are good times to amend the soil (before and after the major growing season). If you use alfalfa pellets you may get a little bit of a smell for a few days after they are added (horse-y stable smell) so best to do it beforehand if you are going to bring your plants indoors. The pellets are clean but not sterile. Anything "sterile" that you add isn't going to help with soil health.
