"You might be stuck with the reverse diode
from input to output. Just make sure it can handle the peak energy
when you charge the 24V output cap from the battery"

I wouldn't even attempt to run the circuit without it. a series diode isn't the greatest idea unless you want to use a Schottky. With only 5 volts headroom a regular diode might result in the battery never getting a full charge.

"I once blew up a $2000 laptop by putting the specified voltage on the
charger input.
Was a bonehead computer design that nobody could have anticipated.
Whodathunk that the charge current regulation was in the wall-wart. "

Oh, my life has been repleat with "whodathunkits". What really gets me about that particular deal is then obviously it wouldn't be able to operate off the wallwart and charge at the same time, would it ?

"And you've
disclosed none....unless I missed that post. "

I doubt you missed it :-) However it is his job to find out of the LM317 can handle the current, and if not then maybe use a pass transistor. In either case, the heatsinking is also his problem. If he wants an amp and sticks a battery that's very discharged on it, a clipon is not going to cut it. We don't even know what type of battery.

Which brings us to those "other issues". I am not even sure yet how a Li-ion battery should be charged. I know some batteries now can be charged faster than you drain them, but we still do not know the particulars here.

Actually after this last power outage I am considering doing something similar with a cordless phone. In fact I'm surprised manufaturers haven't done it. (that I know of) The wallwart is usually 12 volts, so I intend to stack up 12 volts worth of nicads and use a diode and resistor to charge them continuously when there is power. The diode will be reverse biased when there is power and the battery will charge until it floats. Then when the power goes out, the battery wil feed the power to the base to run the phone, and maybe even charge the handset.

Was strange, when the power was out here the landline still worked but the cellphones couldn't get a signal. So if we wanted to make a call we were tethered to the wall. Amazing how unfamiliar that was, after all these years, when it was the norm a while back.

Anyway, this phone idea with the batteries might be useful. I might even be able to sell it. As long as the wallwart puts out DC, it can be done without opening the base. In those cases where the wallwart puts out AC you're screwed.

Next I want a buck convertor to run my laptop off 12 volts, as it takes 19 volts. Should be fairly easy. I am lazy but I will get around to it.