I am currently using BQ500210EVM -689 (760308101 coil) and designing the different receivers with your coils. I am using bq51013 and bq51050 Texas instruments chips. I tested 760308201 and 760308101303 coils and the receiver works fine but with 760308103206 and 760308101208 coils it did not work, you also stated this in mix and match.
My idea is to change the transmitter coil to let's say 760308100110 or 760308111 in order to use 760308103206, 760308101220,...
Please advise me whether this could work with bq500210, just to change the coils or do I have to make more changes?
Your design will mix large TX coil with small RX coil. This is difficult due the coupling factor between coil. The best coupling factor is a 1 to 1 ratio. You would have better performance with a TX coil diameter closer the RX. A decrease in coupling factor will reduce system gain.
This can be offset some increasing the RX coil L, similar to turns ratio of a conventional transformer.
See TI AAJ article SLYT477: www.mouser.com/.../TI-Designing-a-Qi-compliant-receiver-coil.pdf
TX you are using is the older 19V input version, bq500210. If you can transition to 5V input we have more options, see TIDA-00762 and TIDA-00415.