By varying the level of Reed-Solomon error correction, it is possible to encode QR code of different shapes. The exact shape possible will become only only after some experimentation.
About us - we a team of engineers and programmers with over 10 years of development experience in algorithms, machine learning, web/mobile/desktop softwares.
Please contact us over chat for further discussions. In our opinion, it might just be better to develop a proof of concept qr code image before beginning work on the project. Let us know if the idea is agreeable to you.