For .38 Special (or any other round) you have the option to put a powder check die in station 3, then seat bullets at station 4, using the built-in crimp shoulder in the seating die.
For cartridge runout, I have made almost perfectly straight .30-06 on an old Lyman Spar-T turret press. If it can be done there, it can be done anywhere. Failure in this area is primarily caused by two things:
1. The sizing die's expander pulling the neck of the case off-axis.
2. The seating die failing to press the bullet in straight.
For 1., above, there are several strategies.
a.) Take a single stage press and use the Lee Collet die for the case neck sizing (follow that link to see why and to see how much an expander can pull a neck off-axis) and decapping, then use a Redding body die to resize the case body. These are available in regular and small base configurations.
b.) Get a small base Full Length Redding type S die and choose a bushing that just takes your necks down the right amount in diameter so you don't need an expander.
c.), Use a spherical carbide expander, but lube the inside of the neck well, despite the carbide, to minimize pull on the bullet.
d.) Use a standard small base die with the expander removed or ground too small to work, then separately use one of Sinclair's mandrel die bodies with the right size mandrel to do the expanding down into the case rather than pulling the neck out.
To eliminate the seater die runout, get a full-length (Redding or Forster) sliding sleeve competition type bullet seating die; not a half length sleeve type (e.g., Hornady). The Redding adds the feature that the seater stem floats to self-align. I've heard good things about the Forster and it is available in a less expensive form with no micrometer adjustment. However, I have only used the Redding and know it works as advertised
In principle, by holding the case in alignment, the full length sliding sleeve removes any press alignment issues from the equation.
For the powder measure, I can't say I've ever found my Dillon measures to be reliable to 0.1 grains, but you don't normally need that with rifle loads if you have your load averaging in the center of a charge range that has the same point of impact accurate across that range (see Dan Newberry's OCW method
of load development). For minimizing the effect of vibration you can add supplemental powder baffles
. If that still doesn't cut it for you, continue sizing single-stage. Since sizing is what causes final growth in the case neck, you can trim more accurately if you do that anyway. Otherwise you have to pre-trim, and because the cases don't all grow the same amount, that's never exact.
Recently board member Bart B. pointed out you can turn an EZ-Out stuck screw remover clockwise (against its tapered left-hand extraction screw) inside the mouth of a trimmed case to burnish the sharp edges to prevent them scraping jacket metal off bullets. This is good for the bullet and may help reduce metal fouling. As a result, you want the opportunity to do it before passing the sizing stage of the loading cycle.
Personally, I have an inexpensive Lee Challenger press set up that I decap on before cleaning cases. This keep primer crud out from under Dillon's shell plate or off any other press I'm using. It also lets me clean cases before dirt on them can score a sizing die. I then size carefully to omit neck runout. The rest of the loading process may then be done progressively without issues.
That said, if you want to run in the other direction, you can get an RCBS X-die that takes over case length control so you don't have to trim after the first time. You may be able to use a carbide expander kit with that die. This will keep your operation truly progressive.
If your sizing is as difficult as you suggest, look at trying some other case lubes. Original STP oil treatment isn't bad. $1.50 at Wallyworld.