Transit in Frankfurt with an expired US J-1 visa (within 30-day grace period) - Do I need a visa?

Hi,
I have a specific question about transiting through Frankfurt (FRA).
The Situation:

• Nationality: Turkish Citizen
• Route: USA -> Frankfurt (FRA) -> Turkey (Lufthansa)
• Visa Status: I am on a J-1 visa. The visa stamp in my passport expires on Sept 1st, but my flight is on Sept 16th.
• Legality: I will be within my legal 30-day grace period in the USA and will have a valid DS-2019 form with me.
• Transit: I will stay in the international transit area in Frankfurt and not enter the Schengen zone.

My Concern:
I know Turkish citizens usually need an Airport Transit Visa for Germany unless they have a valid US visa. Does the '30-day grace period' and a valid DS-2019 count as having a 'valid visa' for transit purposes? Or will the 2-week gap between my visa expiry and my flight date be a problem at check-in?
I’ve seen some IATA/Timatic info saying expired US visas are accepted if you are returning from the US, but I'm looking for real-life experiences. Has anyone done this recently? Did you have any issues with Lufthansa or German authorities?
Thanks in advance!"