I'd switch to a different powder measure - borrow one if necessary - to confirm the cause. That is the most likely cause, but you can't just guess, you have to know. More on that below.
Weighing finished rounds won't necessarily help as there is a good amount of variation from case to case - you might get by doing it with a small case like a .380, but you'll have to weigh a bunch of uncharged cases to find out how much variation they have (in a recent batch of 100, commercial .30-06 cases can vary by as much as 10grains). If the differences are too small to see on a visual check, then the only way to tell is to charge a bunch in a block of, say, 50 and check-weigh them. With a funnel, you can put the good ones back in and seat bullets in them. It will take longer than usual, but it will confirm what you need to know. If you were finding problems in 2 out of 10, it should become apparent quickly.
Eliminating other causes we can do with the extra information you provided. Crimping is not the issue, unless the rounds are telescoping as they are fed. That is exremely bad pressure-wise, but you would have noticed it and it wouldn't cause squibs. As carefully as you have been watching OAL, if there were insufficient neck tension, you would have noticed variation from round to round. I would store primers in a sealed ammo can with a dessicant pack to control humidity. Neither powder nor primers should be stored where the temperature will get really hot, but as you haven't had them for long enough to see any degredation, and they have all been going off, I would eliminate them as a cause, too. I'm assuming that you are not finding unburned powder or you would have mentioned it. With UNIQUE, you'd have seen it easily and have had to clean it all out of the workings.
The thing about "Max load" is that it is a relative term and in practice is different for every firearm, even two chambered the same. I shoot a lot of older (and antique) military rifles - some of them display pressure signs with starting loads. With handguns, especially semi-autos, the flattening and cupping of primers so easily spotted with rifle cases is not always easily seen. In fact, it is easier to see underpowered loads in pistols when the cases fail to obturate and leave the fired primers raised. Often, when there is an overpressure, the barrel fails (KABOOM) and there are no apparent signs on the brass fired immediately before the failure. With a blowback operated pistol, you can sometimes notice the recoil being sharper, especially with smaller and lighter guns, and the report louder (which is more likely to be noticed by bystanders than the shooter). With UNIQUE, the incremental increases in .380ACP are only .2 gr, and then .1 to max. That is no big deal with a large rifle case holding 40+ grains, but with an itty bitty pistol case and charges approaching max, bridging and overcharge in the next case can cause a small handgun to become flying shrapnel. Fortunately, the Lee design prevents that, but does not prevent undercharging. (Similar comments have been made about the RCBS Little Dandy which uses small cavities also.) With larger adjustable measures, you only have to worry about bridging with IMR extruded powders, and flake or ball powders, even in tiny charges, meter very consistantly.
I like UNIQUE a lot, and have been using it in a Walther .380 that my dad carries for twenty years. It is not a fun pistol to shoot, and the slide has carnivorous tendencies, but he likes it the once or twice a year he shoots it is no big deal. While he may shoot several hundred rounds of .45ACP at a range session, he seldom shoots more than two mags out of the Walther. UNIQUE is my "go-to" powder for most handgun rounds: .380, 9mm, .38spec, .357mag, 40S&W, .45ACP, and it works well for some cast loads in rifles. I buy it in 4lb jugs.
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The light charges seem to have enough powder in them to launch the bullets downrange. If you can confirm that the problem is the powder measure, then they should be safe to shoot, but I would check the barrel after each light load just to be sure nothing is lodged in it. If you cannot confirm the cause, the safest thing to do is to pull them, but I myself would be doing a lot of experimenting with the measure and scales before I pulled 400+ rounds 
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