A few more observations.
1200 fps does seem to be about the limit of accuracy with plain base cast bullets in NEF barrels. Relatively soft bullets; i.e., air cooled WW are called for. In my .45-70s, 50/50 WW/lead gives the best accuracy. I have not worked with this alloy in other calibers.
MUCH higher velocities with excellent accuracy are possible with gas checked bullets and very hard bullets. My .25-06 shoots 100 grain cast GCs at 2300 fps better than any jacketed load I have tried. My Maxed .357 typically shoots about 5/8" 50 yard groups at nearly 2000 fps with 180 GCs.
Cast bullets for microgroove barrels must be well over nominal diameter. I size bullets for the Max to .360 and for the .45-70, I shoot as cast, around .460-.461. My microgroove Marlin .44 Mag gets bullets sized to a bit over .431 and I had to lap out a sizer to get that.
Any copper fouling in the barrel will open up groups with cast bullets. I have noticed that this effect is worst right after the change and gradually lessens as I shoot. Changes in lube also seem to have an effect, just as you noted. I don't think it is the powder or the bullet, just the lube.
You are gonna have to be mighty lucky to get very far with commercial cast bullets in the NEF barrel. They are almost always too small, too hard, and lubed with crappy lube.