You can use Seachem Prime or Safe as your water conditioner when doing partial water changes. It not only neutralizes chlorine/chlorimine, but it will convert ammonia into relatively harmless ammonium. This conversion is said to only last 24 - 48 hours, but that's plenty of time for your bio-filter to process it and fast growing plants, especially floating plants will use ammnium just like ammonia as their N2 source. The downside is that if/when BB processes ammonia/ammonium, it will translate into higher tank nitrates. But the partial water change is still a plus.
You could also pre-filter the water through a product like API Nitra-Zorb, invest in RO or RO/DI, or use a different water source.