My understanding is when it comes to INFI vs. A2; the way to look at it is with handle slabs. The transition from A2 to INFI happened before tubes came in the picture. Smooth handle means that there is a higher chance that your SHII is A2, and a possibility of INFI. Partially grooved handles is the opposite. These knives are most likely INFI with a very slim chance of A2, fully grooved handles regardless of slots or not is INFI.
Dimpling is not a good way to tell if it is INFI or not as the dimpling has to do with the HT and not with the type of steel. Only Busse can confirm for sure.
All battle mistresses were INFI regardless of handle types.
All SHSH's with tube fasteners (original) are INFI. This version of SHSH was made sometime around 1999 - 2001.
The lineage of the handle slabs and screws on the SH:
1. Smooth handles, solid pins.
2. Smooth handles, screws.
3. Grooved handles, screws.
4. Grooved handles, tubue fasteners.
5. Swirl-pattern texturing, tubular fasteners (maybe)
Summer/Fall 1999 to Spring/Summer/Fall 2000 brought all these listed changes. It also brought the change from screw type fasteners to tube fasteners. First the Badgers, then a combination of Steel Hearts/Battle Mistress's.
The original Steel Heart is ATS-34. Not all original Steel Hearts were ATS-34 as they were mostly made from A-2. The ATS-34 models are very rare as less than 200 were made.
My understanding was that there are no BBSHSHs in INFI. However, I’ve sent one to Busse recently and was confirmed to be INFI.
The timeline is: SH1, BBSHSH, SHSHII, SHE, FSH. The SHSHII is called a "two" because it was the second version of the straight handle Steel Heart, the BBSHSH being the first, so the SHSH and the SHSHII are the same. There are also two versions of the BBSHSH, one with a "Humpback" blade profile and one with the same blade profile as the SHSHII
Above are my notes from contributions of the older hogs such as Cobalt and Papathud.