Welcome to the forum.
In general I concur with most of your last post, but follow me in the logic of evaluating the data if you will.
From Berry's website, as I am sure you have read....
""Plated bullets occupy a position between cast bullets and jacketed bullets. They are soft lead, but have a hard outer shell on them. When loading plated bullets we have found best results using low- to mid-range jacketed data in the load manual. You must use data for a bullet that has the same weight and profile as the one you are loading. Do not exceed mid-range loads. Do not use magnum loads. ""
In general terms that means you should be using the low to mid data for 124g FMJ loads or the slightly above min to max range for lead bullets is typically a good recommendation. The two ranges overlap for use with plated bullets. Close bullet weights (a couple or five grains) in load data can be used to determine a reasonable start point.
From the Hodgdon site I see, and you should verify:
125 GR. LCN Titegroup min 3.6 max 4.0
125 GR. SIE FMJ Titegroup min 4.1 max 4.4
The prudent middle ground would be around 3.6-3.8 to 4.0 load, maybe up to 4.2 <but dont start there.
More importantly and perhaps you missed it, the Hodgdon website lists :
130 GR. BERB RN Titegroup min 3.5 max 3.9
I believe if you contacted Berry's they would help you confirm that this listing is for their bullet which is very close to the bullet you have. This range is consistent with what is noted above. The only kicker is your bullet is a HB which means you should err on the low side of a safe min starting out. Which is somewhat addressed by the fact your bullet is 124g versus this 130g.
This tells me you are on the right track with your initial loads. I would consider a different powder if next time, but would not hesitate to work with the Titegroup while you have it.