Quick update on this one.
We sent the tax source correction request to BS as suggested in this thread. They were very prompt and sent us a letter and returned all the documents that we submitted saying that we have missed the date (30 Sep) and they will not be able to process the request.
Somehow, I still decided to send a polite e-mail to the BL tax authorities requesting to consider the full year as our understanding was to file only in BL. They replied saying that BL would only be responsible for Sep-Dec as we were residing in BL for that period only. They did mention that they have forwarded the request to BS.
I thought that was the end of it and BS would not bother replying or just repeat what they already mentioned in the earlier letter.
However, much to our pleasant surprise, we received a tax assessment from BS today considering the full year investment for Pillar 3a along with the refund amount.
Being the first time interacting with Swiss authorities, pleasantly surprised at the speed, efficiency and hassle-free service. Kudos!