Well I had to go look up the bullet you were referring to to see what it actually was. Like you mention it is machined to drop at .356" so that allows you to put on the coating then size if needed.
I use .357-.358 in my two Sig's, (P320,P226TO) with half a dozen different bullets and they shoot them into boring ragged hole groups over several different loads each.
If you use some 400-600 grit wet dry wrapped around a 5/16 or so dowel rod and apply a drop of oil it will polish the sizer out real quickly. Just slide the wrapped dowel through the die and roll it back and forth on the top of your thigh. It goes pretty quick so have half a dozen or so test slugs sitting there to check the sizes as you go. It's easier to take just a touch more out than to put it back.
I would cast your bullets and give them about two weeks to settle into their hardness. Then coat and size. Sometimes they just need a little time to come into the hardness and if you rush things they are all over the place. With my 454, I run an alloy just a touch harder tan straight wheel weights. I have to give them a two to three week span from cast to size before they will act properly. However give them that and they shoot awesome, with no issues what so ever using either the 45-45-10 tumble lube or Carnuba Red from White Label Lubes. I know a lot of folks recommend quenching in water, well I tried shooting both quenched and air cooled and there was no comparison. Air cooled and cured two weeks is the ticket hands down.
All that said, almost any of my cast get at least the two week period now. Not that I decided to go that rout with everything, it just seems to work out that way. When I pour up a batch it is usually around a 15-20# one of each that I am needing. That works out to a LOT of sorting and such not to mention the sizing. If I'm coating that adds another couple of days as once I set up I do everything thats getting coated at once. I only have a small oven that only holds a hundred or so depending on the caliber. Takes time to do several hundred in several calibers much less 10 or more pounds of a particular one.
Give the mold a chance with a bit larger sized coated bullet, and give the alloy a week or so at the minimum to "set" and see if that helps. Also I don't remember what your load was or if you were using the stock barrel or had changed it to an after market one. I use powders like BE-86, AA-5,7, Bullseye, and a couple of more that just ain't popping into my head. These have all given plenty of accuracy and velocity under the powder coated bullets with no leading or tumbling that i have found out to 25yds.
Hope this helps