Welcome to TFL SkipperT.
I'll start by saying that I like your combination. Bullseye or TiteGroup under 115g plated bullets are both great combinations in 9mm for your application (range shooting & competition). So you started off right.
As for data; Speer #14 shows:
Bullseye from 4.2 to 4.7 grains
TiteGroup from 4.1 to 4.5 grains
Starting at the low end should yield something close to your needs (if not, making it). Their GDHP bullet was set to an OAL of 1.125"; and their RN bullet was set to an OAL of 1.135". You said you have a Berry's bullet; but didn't mention the bullet profile (RN or FP). If it's the RN, then your OAL would likely be close to the 1.135; if it's a FP, then your OAL would likely be close to the 1.125.
These Speer bullets are a thick plate. Yours are a thin plate. So it would be advised to not run your charge weights to the top of the scale. Keep 'em on the mild side. Running them mild suits your application anyway.
Plated bullets are not lead. Plated bullets are not jacketed. They are relatively new in the shooting world. Their original intent was a non-barrel-leading (and all the other drawbacks that goes along with shooting straight lead) alternative to straight lead bullet applications. They were never intended to be driven as hard as jacketed bullets. But almost as soon as they came out, loaders started doing so. Driving plated bullets too hard can cause plating breakdown, resulting in copper and lead fouled barrels - defeating their intended purpose. BTW, driving plated bullets too hard is a function of pressure, not velocity. So when the box says "Max velocity 1250 fps" or whatever, it's an oversimplification. Velocity is not a function of peak pressure. But I digress . . .
Turns out, you opened up a point ongoing debate with your first post. As a mostly revolver shooter, when I read statements like "With plated bullets, you use lead bullet data," makes the hair stand up on the back of my neck. That statement by itself without any clarification is a bit reckless. It is extremely important to understand that a plated bullet proceeds down the barrel with more friction than a lead bullet. That difference in friction rarely comes into play - but you need to know and understand it. In 9mm it won't likely make any difference. But in a revolver, with the barrel/cylinder gap bleeding off gases, using low end lead data can result in a bullet stuck in the barrel. Either way - loading for semi-auto or revolver - it's information you need to know and always keep in mind.
When I load plated bullets (and I do - a lot), I use jacketed data (or Speer's thick plate, as above), with the understanding to simply not drive them too hard; i.e. stay off the top of the scale. I prefer this approach.
So I don't mean to complicate things; nor do I mean to start a firestorm. I'm just presenting information that I believe is important for a plated bullet loader to know. Keep in mind that most lead data and jacketed data have a lot of "overlap." It's not like a lead table and a jacketed table will be completely different. What I'm saying is to just be aware that a plated bullet doesn't behave like a lead bullet going down the barrel. When you're making your first rounds in a work up, and you're starting low, just make sure you're feeling recoil and seeing a bullet impact point (be it the paper target, the ground, whatever).