AFAIK: any sulphation that remains, will act as seed crystals for new formations. It will resume much easier, and you don't have to discharge the battery so far down for it to get established.Buy a new battery. Desulphation does not work. Crystals coming off the plates takes material with it, diminishing the capacity of the battery substantially. Thats another story.
As for running your vehicle on a capacitor, it can be done. Maxwell sells a supercapacitor that will work for your application for a couple of thousand dollars. They are sufficient to carry the load.
As for the rest, plain and simple, one of the batterys jobs is to act as a stabilizer for the electrical system. Take that out and as others have said, transient voltage spikes will go to work on your electronics and cost you a lot more than a battery. Bottom line: replace the battery.
Desulphating often works well enough for a trip to the shop that sells new ones.