Strobes work differently than other lights. And I would think that the MegaStrobe DMX would work better than a cheapie strobe(like the Big Shot for example).
I could fathom the fixture initially drawing to pull power and charging the caps for the high discharge bulb to pull from later, but I honestly couldn't imagine that being more than say a minute or two, and even so, it's more for "just in case" or to maybe work in conjunction with a very high frequency DC circuit.
I totally understand the "making every amp/watt" count, as I'm constantly at the wall for sound AND lights. It's like they expect me to do a 3000-seat venue off a single power outlet to do both sound AND lights AND FOH and BACKLINE and monitors. Ain't possible, at least not from an Edison outlet!
My first thought is you're not measuring right. I made some "break out cables", which was essential a 4-wire drier/apliance cable that I sacrificed for this application, using those 30-amp wires to put onto a set of 15-amp Edison plugs safely so I can use it inline for measuring. Then, put your ammeter over I think the black lead?(correct me if I'm wrong, I haven't done this for a couple of years) and measure when not under load and then under load.
I would say using your DMX controller of choice, simply plug in DMX and power for each controller ONE at a time. Measure under NO LOAD, with light plugged in(not active) and then under FULL load. Strobes are a bit tricky to measure, so it's best to have a meter than can hold peak or can average. Both have their strengths and weaknesses(unless you have one that can do both), but strobes are such transient lights that they aren't the easiest thing to measure. Chances are your meter be nailing all the peaks anyways and is hammered by them and just showing the mean average peaking during the test period. This should be sufficient for your working numbers.
Also, doesn't the ADJ manual give you this information as well?
My situation was I have this cheap ADJ strobe that came in the Dynamic Party Pack(which I stopped using due to water damage, long story about a leak in my truck's box). But, when I was using it at shows attached to a relay pack, it was still discharging once in a while. So, I had to really dive deep to figure out that a relay pack doesn't actually deliver NO voltage even at DMX value 0. There is a very minute amount of voltage, under 4 volts. The little strobe would suck it up and then discharge when it gets the enough juice. Anyhow, if you search, it may still be archived here. The solution then was to plug in a small night light with a bulb(any wattage, doens't matter) and sure enough, by doing this, the strobe won't work at all UNLESS I fire up that channel on the relay pack. In my situation, this has provided EXACTLY the desired results. The fact that I got a little dinky night light on the channel is meaningless when the light is on as nobody can see that.
But, I'm looking at the Mega Strobe DMX or some other ADJ DMX strobe to replace that little strobe. Since many of my other lights DO strobe, I'm not in a hurry to get a new strobe, but I do have to say, there is NO substitute for a true strobe for a strobe application.
Oh, and when calculating draw, don't just take the bulb(s) into consideration. It's a good start. You have to take into consideration some overhead to deal with the electronics, especially with DMX fixtures. Typically, it's not a whole lot. Items with motors and servos and other moving parts tend to draw more. Rarely, and I say this cautiously, do the fixtures mechanics and overall operation exceed that of the bulb. I'd say just tack an extra 10% MAX as a fudge factor. But always read those manuals, they'll really lay it out for you, or at least they should.