Unfortunately, the likely solution to this is to keep banging out work at wherever you can gain experience as a software engineer. Modern hiring practices are

Unfortunately, the likely solution to this is to keep banging out work at wherever you can gain experience as a software engineer. Modern hiring practices are too rigid and filter-friendly for you to likely appear as a strong candidate based on the fact you have good accounting experience on top of your growing software skills. What will really help you though, is having friends who work at a bank in the software departments. It's almost always who you know in this world. You need to network, network, network!