It's not a complicated as your making it out to be. For your carbon, just follow the direction on the box it came with. If you are using Aqua Clear (same as I), then the directions are pretty clear. I have followed the same with no problems. About the media filter. This will only trap debris from you aquarium & since you have had problems in the past with your trates, I would just rinse out the media as often as possible, till you get a more stable environment over a period of time where you can start to play with how often you need to rinse w/o having to worry about changes. Plus having a clean up crew will cut down on this.
Once you get stabilized then I would had some crabs. They can handle harsher condition. When you said fish, I was actually thinking fish. Actually fish would be too soon & cause more stress. You got to let your tank recover longer if you want success.
With rinsing the media with certain degrees of water. If you aren't wanting a bio build up in the sponges, then rinse with just regular hot water. There no big drama in hot saltwater & hot tap water. Why would you want to make saltwater hot just to rinse. If you want to keep the bio in the sponges, then use the same water from your tank in a bucket & swirl the sponge in a circle motion letting the water pass through it.
BTW, don't use straight vinagar. Put your item(s) in a bucket & just add enough you feel will do the job & to remove the vinagar just rinse well. Again not as hard as your making it. Good luck, Jessica.