I have bullets that are larger then .444" and even with .0018" thick paper that makes the patched bullet .551+ a smidge and that takes a hard push with the thumb to get it seated. With the OE and Swiss powder I been using less to none compression and I find that tight push into the throat compresses the powder more and I find vertical also increases because of the uneven compression.
I been running them through a custom Lee push through die I ordered at .499" but it came at .4994" close enough

also I have one for my .40-65 that I have to use because of the tight bore it has and that rifle shoots MOA +- with patched bullets I run through the die with no problems with accuracy.
This also makes the underlap of the bullet nice and flat.
Try some running them through your sizing die and see how you get along. I would just as soon not reduce the diameter more than .003" myself.