Measure water before or after adding Malt Extract?

Seeing how your pot doesn't really seem to be large enough to do what you propose, I would add 4 gallons of water and start heating it. Once you get it hot enough to dissolve the DME, I'd add that in and see ho wmuch room you have left.

A measuring stick of some sort would help here to see it now you are at 4.5 gallons or 5 gallons. The DME will take up some volume depending on how much of it you add obviously. If you know the volume post DME addition, then you can go and maybe top of to 5 gallons or 5.5 in the kettle to give you more volume during the boil off. But I don't think you can go to the full 6 gallons.

Take real careful notes on this batch and then you'll have a good idea of how much water you could start with on the next batch. Worry about accounting for boil off on that batch.

After the boil see how much you have and figure out your boil off rate. Then top off to 5 gallons or whatever you normally shoot for (I used to formulate my extract batches for 5.5 gallons in the fermentor).

Don't forget that you'll need headspace for the hot break, otherwise you'll be risking a boilover. Especially if you're not quick with a skimming device and able to easily control the heat right at pre-boil (remember that electric eyes will carry over a bit).

You might be better off aiming for a 4 gallon batch size or doing a more concentrated boil and topping off with pre-boiled water in the fermentor. You may have to revisit your hop calculations if you do the latter, though.

Unless you're putting tons in, I don't think just DME will add a full gallon to the volume.