First Robert, let me say sorry for starting to help and then falling off the internet. I had to be away for a couple days without access.
The original problem... Based on what you've posted, just hook the float charger to the battery and power your circuit from that. Your siren won't care about voltage from about 10 V to about 15 V.
A sealed lead acid battery can remain on a float charge forever without damage. Large commercial systems do it all the time - for example the telephone system works this way. Hook up your trickle charger to the battery and measure the voltage - if it's between 13.2 V and 14.4 V (2.2 - 2.4 volts per cell) you are good to go. Cars are usually 13.8 V.
The current required for multiple LEDs is an old problem, and the reason "scanning" LEDs was invented. You basically switch them on and off fast enough that your eyes don't pick up the blinking (anything over about 100 Hz). You use about a 10% duty cycle and increase the current a little bit if you wish. You can experiment to adjust perceived brightness. You will end up with less current than the LCDs.
I'll see if I can sketch you a VFET circuit when I have a second - still catching up on email.






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