Mel's Mix works great. The key is to use really good compost. Well composted horse manure works great if you don't have your own compost heap. Don't buy "compost" in bags at the hardware store. It's not going to work, you gotta use real compost.
If you have a problem getting peat moss or have an environmental objection to using it, the coconut fiber substitute works well, maybe even better. It usually comes in dried "bricks" or blocks that you have to soak and then work it to get it loosened up, but you have similar problems with peat moss if you buy it in compacted bales.
Mel's mix is not cheap. Both vermiculite and peat or "grow coir" are expensive. Be sure to get the coarse grade vermiculite. There is also a fair amount of work involved in mixing the ingredients together to fill you beds, but once you've done it, the mixture works very well. The medium is loose and airy, holds both water and nutrients very well. Since you don't walk on it in the SFG method, it doesn't compact and remains easy to work with using only hand tools or even just your fingers.
You may want to include more than one kind of compost for a variety of nutrients. Chicken manure (not too much, obviously), worm castings, kitchen compost, mushroom compost.
When you harvest a "square" you work in a couple handfuls of compost to replenish it. If you're using good quality compost, you don't really need to add fertilizer. You can spray it with kelp juice or sprinkle in some dried seaweed if you really think you're missing trace minerals. But I think there's gonna be plenty of "traces" in the compost if you are using good stuff. Again, the stuff at the big box store nursery isn't going to work for you here.