I personally believe nothing can be attached to a disk because it is indeed some sort of space with different physical properties. That is exactly why it's perfect for a 'floating' chariot.
All you need is somebody who can cut wood. Just make a round platform slightly larger then the disk. Make sure that the edges are thicker then the rest of the platform. Cast disk, put platform over the disk, attach harnas/ropes/whatever to the wooden platform, cast phantom steed and enjoy a custom chariot.
You can make this a whole lot better and stronger if you're willing to put some time and effort in it. As long as you're basically making some sort of platform/lid to put over a disk it works fine. It really is not that complicated.
For the people out there that want something awesome at lvl 5.
Get 4 players to each play a small creature with at least 2 who can cast disk.
At the front end make a box large enough for 2 mastiffs per player (mastiffs are legal mounts for small creatures). So with 4 players that means 8 mastiffs have to be able to fit in the box. You don't need any joints or whatever. Just 1 large box with the platform attached at the back end. Make sure that the platform at the end is high enough so that you can look over your 'engine' box.
Put a repeater bolt thrower on it.
Cast enough disks to reduce the effective weight of the construction+passengers to almost 0.
For extra defense cast all defensive spells on it that you have.
You've just made a 20ish feet long medieval tank. Because it weighs nothing turning is a breeze. The engine is 'safe' in a box. Your whole party is standing at least 4 feet in the air on a platform with a repeater bolt thrower and you can run as fast as you can throw sausages in the engine.
When you hit lvl 6+ you can make some seriously awesome tanks this way. And for those wondering yes this was the beginning of a beautiful story :D
edit: tip: disk floats at 3 feet above the ground. Disk that have to much weight on them dispell. Make sure you to put your tank on some supports that are just a fraction above where the disks are hanging. When all disks are in place, throw some food to your mastiffs, they will pull the thing from their supports and make it land on the disks.
You can go crazy here and make retractable supports or use simple blocks of stone. It's just something to think about when you're building a tank.