You have a 2kwh ebike pack? That's huge, sure it's not a moped?
And using an inverter is a sure fire way of losing a lot in inefficiencies. First the extra weight 2,5kw inverter (5kg?), I'm guessing 75-80% efficient, losing approx 400w in that step. Then the charger efficiency... It's probably higher than the inverter, but around 90%, so 200w. Totalling an approximate 600w loss in heat.
I don't think the equalization is going to be an issue, charging is done separately. And the voltage diff is going to be so small, we're not going to see high equalizing currents.