OK.  I have received the tomato powder and have all the ingredients ready to give it a test drive.  This morning I did a quick experiment to determine the approximate amount of tomato powder to add to water.  I compared Campbell's Tomato Juice against filtered water with powder added.  Both were room temperature.  It appears that the ratio is somewhere in the 2 tsp/100 ml range in order to match the viscosity of the commercial juice.

One note:  the powder/water mix wasn't as tasty as the commercial tomato juice.  I attribute this to there being salt in the commercial product.

So if that is correct, let's revise the recipe one more time:

For 1 Nalgene bottle of Bloody Mary's:

270 ml Vodka
Packet of bloody mary seasoning mix
7 tsp tomato powder (2.33 tbsp)
Fill to top with water

Shake to mix, drink!

I'd test it out right away but it's a bit too early in the day to get on the bottle.  Thankfully a weekend soon approaches and I can give it a proper test.  I'll try it first without adding salt, then try salt on the second time.   Probably not on the same day though.