That is a bit of a mess, isn't it?
Usually the reefing line at the clew terminates at the boom directly below the reefing clew. The line goes straight up to the clew, through the cringle, and then back to the block at the end of the boom. When you grind in the reefing line it pulls the reef clew *both* down and back.
On my boat I run the vertical bit of the reefing lines on alternate sides of the sail for the first, second, and third reef. The first reef has the vertical bit on the port side, the second reef on the starboard side, and the third reef (which I only rig offshore) on the port side. The rationale will be apparent shortly.
Battcars stacking up is an ordinary issue for the tack. Usually (there's that word again) the tack rings are between cars so you can pull a roll of sail down to the reefing hook and get good luff tension when you haul the halyard again. I have seen some boats use a cunningham for the tack but that can get messy.
You will get most flexibility if you have tack hooks on both sides of the boom and tack rings that can be made on both sides of the sail.
When putting in a reef hook the tack on the same side of the boom as the vertical part of the clew reefing line. This is a minor detail that borders on obsessive, but it allows the bunt of the sail to hang on one side of the boom and not distort the shape of the reefed foot or the sail to chafe on the boom. It also makes tieing up the bunt with the nettles (the lines through the reef points in the sail) easier. The nettles are not supposed to take any load -- they are just there to tidy up the bunt of the sail. In fact if you can you should tie the bunt without going around the boom. Clearly you do have to go around the boom if you have a wire-type foot on your sail.
Reefing is a bit easier by alternating sides, and on my boat the sail is distributed sufficiently that I often don't bother tying in the nettles. There is a bit more work on the second reef to reach around the mast to get the tack ring on the hook on the starboard side (main halyard winch is to port, so I work from the port side) but overall the approach I have outlined is effective, reasonably fast, and can be employed safely.
Two of four crew did almost all the deck work during a transatlantic crossing on my boat. We went through a good bit of weather between Falmouth and Azores. Either of us could get a reef in or out within two minutes by the time we pulled into Horta. Practice makes perfect (or better anyway) and I wouldn't be surprised if it would take me four or five minutes today.
sail fast, dave