Typically, 5.4 is a great middle ground for beta and alpha. For higher gel temp grains (which I've been finding a lot lately with Weyermann), a higher mash pH might help with attenuation, 5.5 to 5.6.What mash pH should i aim for? cheers brewers!
There are a couple things I'd change in the recipe...
1) I'd skip carapils. Go pils and munich 1 for color
2) Typical commercial Northern German pilsners will not have late hop additions. All IBUs will come from one early hop addition, anywhere from start of boil to 45 minutes. For Bitburger, I'd go 30 to 35 IBUs with Perle or another noble hop. If I had to guess, the recipe was created with those late addition hops because the attenuation wasn't great
3) Which brings me to my next suggestion. OG should be closer to 1.046 and FG should be closer to 1.007. This beer needs to be super dry. Sweetness will hide the hops, which is why I mentioned the hop schedule in #2.
4) Pitch a ton of yeast. I use a pitch rate of 2.5m cells per mL of wort per °P which ends up being close to 100B cells per gallon of wort.
I actually brew this beer a lot as Bit is my favorite German pilsner. I can't compare OPs recipe since I haven't brewed it but with the suggests above, this beer is as close to Bit as a home brewer will get.