I use the electrolytic rust removal technique all the time-actually just finished up a wood burning stove resto a few weeks ago that turned out killer. Looking at your setup, I have the following tips for you:
1. Wire brush that rebar-it has an oily coating over some dull grey stuff that you need to wire brush off to make a good contact. I just use an angle grinder with wire brush-you will need to clean them up periodically too, once the "sacrificial anodes" get rusted up too much and the process slows down.
2. You don't need to use that spendy copper wire, rebar aka bailing wire works fine and is soooo much cheaper. Use a big coil of it around each rebar piece, for maximum contact.
3. As already mentioned, use battery charger(s) hooked up to batteries and the batteries hooked up to your project. The battery acts like kinda a buffer and prevents the charger from shutting off. ALSO, I have found that old school needle gauge chargers (with NO auto shut-off) work far better than newer ones. You can find them at garage sales or swap meets for dirt cheap.
4. Rebar as anodes work great but my favorite are pieces of "extruded mesh" because of it copious amounts of surface area. It's also easy to clean up between sessions, with the angle grinder brush I mentioned. Another great anode is an old Briggs & Stratton flywheel-they fit perfect in the bottom of a 5 gallon bucket (I used flywheels I don't need with fins broken off). I mounted a thick wire to it, in one of the screw holes, and set it at the bottom. Remember, you want as many angles around the object covered as possible, so it gets all the surfaces. Also, ONLY USE FERROUS METAL FOR ANODES! (i.e. iron or steel with no coating). Stainless steel leaches off chromium, if used as an anode, and is very very nasty and toxic.
Don't make your own backyard EPA superfund site!!
5. Periodically examine the piece you are cleaning and wire brush that black slime off them to speed up the process. You will know when to have to clean anodes or the item, when the bubble-n-swirl of the electrolysis diminishes (and by the gauge on the battery charger)
6. Wire brush off any black slime, dry, and lightly oil the item to prevent flash rust.
7.
SAFETY NOTICE: This process gives off
highly combustible Hydrogen gas, be VERY CAREFUL of makes sparks if moving stuff around in the tank and don't do this process in a confined space.
Hope these tips help! Here are pictures of my latest electrolysis setup and project. I hope to yet build an even BIGGER tank setup for doing entire mini-bike frames! (p.s. ignore the mixed up wire colors below, negative ALWAYS goes to the item you want to save and positive to the "sacrificial anode(s)", which will rust up fast-don't mix them up!)