I have three EAA Witnesses (Tanfoglios) in .45 ACP. It has been my experience they prefer target-grade ammo. I have a lot of .45s and therefore a lot of ammo in .45. I have found that all of my Tanfoglios shoot well with a 230-grain LRN bullet over 4 grains of Bullseye.
By "shooting well" I mean groups under one inch at 10 yards. In the gun I settled on in comparison with yours, it would be the standard version, full-size. I quite trying to develop a load for it when I was under one inch at 10 yards.
My Elite Match, which is one step up in the product line, gets down to 3/4-inch at 10 yards. My rangemaster gets irritated when he sees the gun on my table because he knows it means he will be making new backboards for targets because I will leave him with one big hole in the middle.
My poly-compact is the most accurate of the lot. It will shoot 1/2-inch at 10-yards with very little effort.
In sighting in and shooting the guns in competition the one thing I feel I've learned about Tanfoglios is that they prefer target loads. If you are a handloader start 15 percent over minimum. If you are buying OTC look for the lightest load available.
In some ways I'm not a really good guy to respond. I shoot for accuracy. When I buy a gun I buy a Wolff calibration spring set. I experiment and find out what works.
I will say this. My firsthand experience with a Tanfoglio was about six months ago. I got it cheap at a show. I've always been a middle-of-the-pack shooter and happy to be where I am. Since the first time I shot a Tanfoglio I've won every match I've entered.
Maybe it is a mental thing on my part. My last win in IDPA was at least six years ago. I change guns and I've won ever match. OK, I'm not in the same category, but I'm in the one a bump above when I shoot the Tanfoglio.
My first EAA cost me $300. I put in $200 in upgrades after it shot so much better than I expected. I bought an Elite Match and transferred the upgrades and more to the new gun. Now I have about $800 in my match gun. I've won every match I've shot this year (7).
If I was to buy "hunting" or "self defense" ammo for the gun, I'd go with what shoots straight. I carry the Match every chance I get. It's loaded with woefully underpowered match ammo - it hits my target every time. A miss with an HP is a miss. A hit with a sluggish .45 ACP is a hit.
Look for target ammo. If yours is like mine it will hate every form of SWC. Ball will be great though.
Try some lead bullets. I've been very happy with them.