B&W 801 series 80 batteries?

Here's how they work.First thing - series 80's are not a APOC as used in later 801's and other B&W's. The 80's protection circuit is powered by the battery.If you beat the guts out of this speaker ( with a 9V battery installed) - the speaker will disconnect from the amp (no sound) and the red LED will light up. Turn the volume down and hit the button that has the slash thru the lightbulb and the red LED goes out and the speaker comes back on.The button with simply a lightbulb icon on it apparently is a test button - press it and the red LED lights and the speaker disconnects from the amp. Again -reset by pressing the ligtbulb with slash thru it button.
Later APOC circuits charged a capacitor when you entered the idiot range and disconnected the speaker from the amp and lit a LED so that those truly impaired might notice another symptom beyond the lack of sound.No button needed to reset - just turn down the deafness control and they come right back on.
I'm not sure how great the old relays in these protection circuits sound ( maybe ever sounded?) - but most of the APOC equipped speakers are getting tough to source replacement drive units for - so removing the APOC circuit is something you probably would want to at least think about a bit before hauling out the soldering iron?

Based on Stonedeaf's info that the APOC circuit uses relays, a battery with one quarter the current spec of the original battery may not trip the relays, or trip just a few times then go dead.
This is just a hunch, so you may want to try the lithium batteries and see how long they last in actual usage.
If they are pin & size compatible, any battery is better than no battery.
Good luck

Does the whole speaker have to come apart to access the battery? Also in the end should I just leave well enough alone or is it really worth it soundwise to either replace the batteries or disconnect the circuit, or just leave well enough alone?

Geting at the battery is pretty easy.
1.) Use a coin to loosen and remove the bolt that goes down thru the center of the head. It's got a fairly long thread on it - so when completly loosened you'll be able to simply pinch it with your fingers and remove it.
2.) Lift the head off the speaker a few inches - it's got a coiled connecting cable plugged into the top of the bass box.Pull on the plug at the bass box end of the cable - it may be somewhat tight - but will pull straigt up out of the matting socket. Plug is polarized with a notch - so you can't plug it in the wrong way.Don't pull on the cord itself.
3.) Lay the head aside.
4.) The fabric frame is held onto bass box on the corners by a pretty sturdy rubber gromet and metal post combination. From the bottom of the fabric frame- Pull up on the corners and move around the box and you'll find it simply pulls off from the top.
5.) You're going to see a circuit board with two "button" switches on it and a LED - right behind that will either be a long dead ( maybe leaking) battery or a pair of battery leads/clips. This stuff is all located on the right front top corner of the bass cabinet.
6.)Somewhat to my surprise - the batteries are available - must have some industrial application I'm not aware of?
7.) Would suggest replacing them - since in no way will this affect the sound over no battereies at all - and s$#t happens! You have a perfectly functioning and quit wonderful sounding set of speakers -but very understandably - factory parts are no longer really available for the woofers or mids and the tweeters require a X-over replacement in order to be replaced. A working protection circuit just seems like it's worth the trouble.

Thanks for the great info. Do you think bypassing the circuit is worth doing soundwise? Or would it not be noticeable enough to be worth it? I had one B+W rep tell me yes and one tell me no so I am interested in your take on it.