Skyhawk,
Your experience is not uncommon for brass that was fired in an as-issued Garand chamber (match chambers don't do it). I've had it happen even using my Forster Co-ax press.
The Garand as-issued chambers are often long and wide at the breech, so when you size the brass, the required additional narrowing lengthens the case enough that when the die shoulder sets it back, moving that much hard mil spec brass around seems to create some extra springiness. It's the same problem people buying once-fired brass can run into, especially if it was fired in a machine gun originally. It just won't size down to spec on the first pass through a standard die, so they get a small base die, fire it once in a commercial chamber, then don't have the problem using a standard sizing die afterward.
I've also brought brass down and additional couple of thousandths by running it through sizing a second or third time. If your Loadmaster's linkages allow, you can run the brass up into the die, then hold it up in there for a count of few seconds to relax, withdraw it just enough to get your fingers around the base, turn it 180° in the shell holder, then run it back up into the die again, and give it a few more seconds. It will often come out a little shorter.
But here's the important question: was this brass fired in your chamber originally? If so, even though it doesn't meet SAAMI specs, it is probably shorter than it was before you resized it by at least several thousandths. You only need it shorter by about -0.002" from its ejected length to feed reliably. In fact, sizing it more than that is pretty much just overworking the brass and shortening case reloading life and making you need to trim more frequently. Sizing it to make the case gauge happy is only important if you want to be able to fire it in other guns, some of which have SAAMI minimum length chambers.
To see if you are shortening the cases enough, you need a case comparator to see how long the case was before you resized it, and how long it is afterward. You can buy a
commercial comparator adapter for your calipers to let you see this length difference (the difference is all you care about; not the absolute numbers). That's convenient because it has a base with a set screw that retains it on the caliper. But you can also improvise with a 3/8" diameter spacer or bushing journal, as shown below. It's a little clumsier to juggle two loose parts at once in your caliper, but if you only need to verify this enough to get your press set up and are then going to leave it alone, it's good enough. Just take several before and after readings to average and verify the results.
(NOTE: That particular spacer is actually rather bigger than 3/8" ID. It's about 0.409" ID. I'd recommend something closer to actual 3.8" (0.375") for the .30-06 brass because of its slightly narrower shoulder. I 3/8" ID bronze bushing journal is a good choice if you have a hardware that still carries them.)
Finally, if you feel you do need to size brass down all the way, you can get the mouth of the Lee die ground shorter. They aren't expensive to replace, so it's not an unreasonable thing to do.