It sounds like you've been thorough in trying to diagnose the issue with your 2008 BMW R1200GSA, especially considering that you've swapped coils and injectors without improvement. Given the symptoms you described, here are some potential causes to explore:
1. Clutch Issues:
Worn Clutch: A worn or slipping clutch can cause a strange feeling when pulling away from a stop, especially if the issue progressively worsens. At 50,000 miles, your clutch could be worn out, particularly if you've done a lot of heavy riding or off-roading. Consider inspecting the clutch for wear or damage.
Clutch Splines: The clutch splines could be wearing out, which might cause intermittent engagement issues. This is common in higher mileage bikes.
2. Final Drive Problems:
Drivetrain Wear: Another area to check would be the final drive. Any wear in the final drive components can cause unusual sensations when pulling away or during transitions from idle to throttle.
Minecraft APKShaft Drive Issues: Inspect the driveshaft for any wear or damage. A damaged driveshaft could contribute to the strange feeling you're experiencing.
3. Throttle Body Sync:
Misalignment: Even though you've swapped injectors, the throttle bodies may be out of sync, causing uneven power delivery at low speeds. It might be worth checking the throttle body synchronization.
4. Fuel System:
Fuel Filter or Pump: If your fuel filter is clogged or your fuel pump isn't delivering adequate pressure, it could cause inconsistent performance. Check for any signs of fuel delivery issues.
5. Transmission Problems:
Gearbox Wear: Issues with the gearbox, such as worn bearings or gears, might cause unusual sensations when engaging the clutch or shifting gears. Inspecting the transmission could be necessary.
Given that you've swapped components like coils and injectors, focusing on mechanical aspects such as the clutch, final drive, and drivetrain might help pinpoint the issue. If the problem persists, it may be worth taking the bike to a specialist for a more in-depth diagnostic.