Holy cow, my heart sank when I read your post! I know this doesn't help you directly, but I'm using an R7 with a 400 4 DO version 1 and get great results with af accuracy. Only slightly less accurate with a 1.4x EF II. I would say that the research I've done suggests the 300 2.8 mk 1 with 1.4x II is similar to the performance of the 400 4 DO mk 1 optically, with your combo having slightly better micro contrast than mine. Take that with a grain of salt since I'm just regurgitating what I've read. I think the relevance here is to point out that my 400 DO is razor sharp on my 20mp full frame 6D, but shows its limitations on the cropped 32mp sensor of the R7. With such a super high pixel density, the R7 starts to show the optical limitations of my 400 and my other early generation L series glass. Those lenses just weren't developed with such a sensor, most actually developed when film was the standard, although I'm sure you understand that. I'm still happy with the R7, though. It nails eye focus like nothing I've ever used. Even though it does miss a bit with faster moving subjects, it eventually locks back on for me and still lets me catch good images. If I had to do it over, I'd buy the R7 again even with the known occasional drifting af.
Because it's an older EF lens, same as your 300 2.8, the frame rate is slowed from the maximum limits for designed RF lenses. I seem to be routinely achieving 8 fps in EFCS mode, and 13 fps in electronic mode. Plenty fast for me.
I've only acquired the 400 DO recently, so I'm still learning its limits, and sadly haven't had much bird time with it yet. However here are two reasonable shots with the R7+400 DO. The song sparrow includes the 1.4 EF II, the white throat is the bare lens. I hope others chime in who have used your actual kit. Sorry again about your lost gear.