Does anyone have any suggestions with some of the other lead-free options.
Yes. I tried the Hornady GMX in my 300 WSM- Browning A-bolt.
Those were fired into water-filled gallon milk jugs sitting end to end @ 100 yards. Velocity was right at 3100 fps.
Group size was right at an inch, plenty small for a magnum, and all the better that Browning skinny barrel could do.
Hornady says the low end of the velocity is around 2000 fps, IIRC. But the streamlined shape makes this a long range bullet in a magnum. It might make a difference for an -06, limiting range for it to open reliably.
The Hornady and the Nosler E-tip are guilding metal bullets. Barnes are pure copper. Therefore the Horn. and Nosler will not foul as bad as the pure copper Barnes. Besides, the relief rings on the Hornady bullets, make for less bore contact, reducing fouling, drag, and heat.
I would take a long look at the 150 grain Hornady GMX for the -06. You can drive it faster so it holds velocity longer. Another thing is the longer the bullet the higher twist rate that you need. That long 180 E-tip might be marginally stable, hence the lousy groups.