Is there a good technique or tool to keep long macrame threads from getting tangled?
You don't need to work with cord that spans the length of your entire project
You have a couple of options that depend on what aesthetic you are trying to achieve and what you are willing to accept as far as look.
Adding cord with knots
There is a family of knots used to add in new cords to your project. Mostly suggested as a means of adding more colours or something like a handle. Regardless this is to show that you can make changes on the fly. Something like the fisherman's knot you could use to start and stop cords.

Looking at the linked page above you will see many other knots. I only showcased the fisherman's as I am familiar with it as far as connecting two cords goes.
Beads
Only issue with adding cords is that you still have to hide the ends. None of the knots I found that are used in this way were accompanied with end hiding instructions.
From what I understand beads are used for flair. However you could easily hide ends inside the beads as well. If you tie a bead close enough to neighboring knots the bead will not be able to slide around. Then you can hide cord ends inside the bead(s). Gluing it inside the bead could also help.
Splice your ends
A better solution would be to splice your ends. You can do this with either sewing thread or, preferably, strands of the cords you are using.
If sewing: pin the cords ends with their butts facing each other to prevent them from moving and get proper alignment when completed. Get the first few stitches in, for stability, and remove the pins so you can finish.

It's same principle using the cord in the project. Pull out a strand and use that to bind the cord ends. Since you are using the same material you can hide the connection easier.

In either case you should stagger the cuts so that they don't all stop at the same point. This will help with the overall strength. Also, it will be easier to hide individual splices inside other larger knots.