Operate LEDs for long time with batteries

Light is electromagnetic energy. Batteries store energy. You can never create more light energy than the energy stored in the battery. In fact there will always be less because no conversion of battery energy to light energy is 100% efficient. Actually it will be much less. So what you're asking for, defies universal physical laws.

Also, with rare exceptions, exceptional performance increases the cost of a device and you say you want to keep the cost down. Can you see the contradiction in demanding both low cost and high performance?

Get used to it, you will be a happier experimenter.

Maybe you could turn it on only when someone is there to actually see it, using a proximity sensor.