I found out something interesting. As you said, reflection probes work in a way that the probe’s reflection is transferred onto the affected object. This makes a kinda unmovable reflection on an object. Now what I’ve just tried is changing the Reflection probe’s type to Realtime, Refresh time to Every Frame, reducing its cube size to 1x1x1 unit and made it a child of the affected object (with the probe’s local position set to zero). This resulted in an accurate real time reflection of the object’s surroundings that is updated every frame to match the object’s new position. I thought its worth sharing - what do you think about it? 
Wow! Nice work. Could you send us a video?
How much of a performance impact does this have, do you know?
Standard setup:
Mobile probe setup:
Are the videos visible? I uploaded 2 mp4’s but I can only see the navigation bars (it is possible to download after right clicking tho)
I see it just fine in my browser. Awesome stuff! And it looks like it only costs you about 4FPS. Great work.