Thanks to all those who offered suggestions. With clean brass waiting, I went out yesterday and bought some N110 (for my .44), some N135, CCI Large Rifle primers, and 25 Lapua Scenar 155gr HPBTs. I hope to also get some of the Sierra Palma Matchkings in 150gr. Later, I may also try a small slection of 168/175gr bullets.
It's clear to me now that it is unrealistic to nail my ideal L.R. load "right off the bat", purely by looking at spec sheets, but hopefully, I'm in the right direction.
I'm also aware that my standard of accuracy leaves a lot to be desired, and I don't yet have the consistency to show up short-comings in my ammo, so that too will have to change!!
Now I just need a shell holder for my auto-primer and I can load some!!