One thing I see on your setup is that your chainrings have been changed from the original Shimano rings. It could be the spacing between the two rings is slightly different than the originals were, which is causing some of the issues. You mention that your large ring is 46T. Lowering the front derailleur may also help somewhat assuming your original chainrings were 50 or 52 tooth rings.
It sounds like the shifting issues may have only been occurring after the rear cassette & chain replacement. It could be that the pins on the inside of the large cog aren't catching the new chain very well.
I don't have tons of experience with adjusting derailleurs, but I recently swapped out my crankset from a Bontrager (SRAM) 52/39/30 triple to a Shimano Ultegra 5600 52/39/30 triple. I couldn't get the original set up to shift to the largest ring reliably at all. It would often just grind the chain against the large ring when trying to lift to the large ring, then if I adjusted to allow more outward travel from the derailleur, the chain would regularly come off the large ring. I tried all sorts of adjustments for weeks without satisfactory results. Once I installed the used Shimano crankset, and shifting is now basically flawless after the initial setup. The Bontrager chainrings on my original crankset didn't look very worn, but in my case the shifting performance of the Shimano chainrings has been lightyears better.