I used to grow Jalapenos and Habaneros and some Thai Bird-shit chillies in my last house in 15cm or so deep containers hanging from the wall by brackets..I had no problem but there was plenty of sun.If you could bracket the containers OUTSIDE your window you may be able to lower the containers and go for a bigger container and get better results.
My serranto,Scotch bonnet and jalapeno seeds have just popped their first leaves..it is all on again.In containers outside again.
I think getting a lot of sun really pumps up the heat in the chilis too.