You say the die is bottoming out? I think you maybe have full length sizing die instructions and collet die instructions confused. A full length sizing die has a mouth position fixed by how far down you turn the die body threads into the press threads, and it can bottom out. The neck sizing Lee Collet Die has the bottom of its sizing collet sticking out out of the die body and it is not fixed. The deck of the shell holder is supposed to make contact with that protruding portion of the collet and then push it up further, sliding it up into the die body. That action is what pushes the collet nose against its angled closing surface in the die body. If you aren't doing that, it isn't closing the collet to size the neck at all. That would explain the loose fit.
Watch the Lee help video on setting up a Lee Collet Die
Watch the Lee help video on setting up a Lee full length sizing die
If, on the other hand, you are indeed pushing the collet up until the shell deck meets the die body because you have pushed the collet all the way up and you still are not getting any sizing, then the wrong collet is in the Collet die. By disassembling the die and measuring the length of the collet, you can then call Lee and verify that it's wrong and you can expect they will replace it for you.
The Lee Collet Die is a great tool when properly used, but there is a learning curve as to squeeze pressure and feel. Because of that, the Lee Collet Die is not the die I would have started with as a beginner. The regular full length sizing die is what I would have started with, though it does require the extra step of lubricating the cases.
You said you cannot meet the .30-06 minimum length. Both the 30-06 minimum COL , 2.940", and the maximum COL, 3.340", given by SAAMI in their drawing
are to assure fit into, and feed from, SAAMI compliant magazines. If you are loading singly, one-round-at-a-time, they don't mean anything. Some folks have fired full wadcutters in the .30-06, seated flush with the case mouth. Some have fired VLD bullet shapes with very long ogives seated out well beyond the SAAMI maximum. The former won't feed reliably from a magazine and the latter is often too long to fit into a magazine designed for SAAMI standard compliant .30-06 cartridges, and that is why they must be loaded and fired individually. If you are willing to do that, then the minimum may be ignored completely down to case length, and the maximum will be determined by how far out you can seat without jamming the bullet into the rifling.
The maximum velocity numbers for bullets are very, very rough guidelines. What determine whether or not a bullet is upset heavily and starts to foul badly in a bore is the maximum pressure on its base and the roughness of the bore. The same load that produces the maximum acceptable pressure, if fired in a pistol with a 2" barrel and then in a carbine with a 20" barrel, will produce two very different velocities, but fouling deposited or bullet deformation that occurs inside the bore will be the same. What will be different is how many RPM the bullet is spinning, and if it is soft enough, a higher velocity from the carbine, assuming the same rifling twist rate, could cause a softer bullet to deform in flight from centrifugal effects.
So, what velocity should be called the limit? Well, what barrel length and rifling pitch do you use? How rough is your barrel? To complicate things further, different powder burn rates can produce the same velocities, but have different peak pressures. As a result, maximum velocities for a bullet really only apply to one kind of powder and one rifling pitch in one length of barrel in one sort of condition. When velocity limits are published there are assumptions being made that you are using a typical barrel length in typical condition, a standard rifling pitch for the cartridge, and a typical powder.
What you have to do to determine maximum velocity in your gun with your components is to start working loads up at the low end, watching for increases in fouling and watching for groups to start opening up. Those will determine upper limits with your choice of powder, and what the maximum velocity is going to be in your gun, with that powder, is whatever you measure at that point.
For softer bullets in the .30-06, I'd recommend trying to get your hands on some IMR Trail Boss powder as a starting point. Save your 4320 for jacketed bullets. Follow these instructions with Trail Boss
and you will have some good practice and small game loads. You cannot safely compress Trail Boss, so it may never get you to an unacceptably high velocity in your rifle.