You have a good start here, here's a few things in addition to most of the above that I have kept in my Bug Out Bag, and in each of my cars as well, over the years.
Small bottle of alcohol based hand sanitizer.
Small sewing kit with three needs, two different sized straight, one curved, few feet of strong white cotton thread, and same of black cotton thread. Drag thread through hand sanitizer and use as sutures if needed. Couple of buttons of different sizes very handy also.
Burt’s Beeswax Chap stick. Very useful, prevents chapped lips, can seal small cuts like shaving nicks, use as fire starter aid, lube zippers, screw threads, prevent rust on guns and knives, make a candle out of it, put some on the top end of your bow drill and in the socket it fits into on the hand piece to reduce friction and add speed to the drill, wax the bow string so it grabs the drill better too, soothe a sore nose if you have been blowing it and it is raw, prevent blisters by rubbing some on hot spots before they become blisters, use to prevent snow blindness by mixing with small amount of ash and rubbing below the eyes on the cheeks, get a stuck ring off a swelling hand, waterproof leather, clean eye glasses and fog proof them, etc.
Small tube of Preparation H. In a bug out condition, stress and a changed diet, lack of sufficient water, etc. can easily cause hemorrhoids, and you can use it on cuts too as it shrinks tissue and helps stop bleeding.
Small bottle of something like edible mineral oil laxative (can also be used as lube on screws, zippers, etc.) , so if you get bound up by stress, lack of water, etc. you can get unbound, and some Imodium AD for those times when the food or stress gives you the Texas Quick Step, Pepto Bismal tablets for the same plus they help with nausea.
Small tube of Super Glue in a small zip lock bag (in case of leaks) lets you do some temp fixes on things (like glasses by wrapping floss around the broken temple then coating it with super glue) and very good for sealing wounds/ cuts, (was invented for that actually) great on paper cuts by the way!
Tooth brush, dental floss, small tube of tooth paste. Keeping teeth and gums healthy prevents loss of energy and the increased potential for illness to set in. Tooth paste can also be used as a polishing compound on metal, plastics and glass if need be, and the dental floss as a suture in a pinch (yah, had to do that once! Wasn’t pleasant but it worked.)
Foot powder, like Gold Bond, gotta keep the paws clean and dry , can’t run, walk, fight, live if the paws are blistered, infected, etc. Spare pair of wool socks so you can change into them when the ones you are wearing get wet helps with this a lot.
Toe nail and fingernail clippers, and small diamond impregnated nail file, gotta keep the nails from growing too long, splitting, tearing into the quick, etc. and same for the toe nails, getting an ingrown one while on the march is bad news.
Package of unlubricated condoms, put one inside a sock and you have a water carrier/storage device. Can also be used over the muzzle of a shotgun or rifle to keep mud and debris and water out.
Small unbreakable mirror, for signaling and for checking parts of the body you can’t otherwise see for ticks, fleas, injuries, etc.
Small magnifying glass, start fires, see splinters, etc.
Good pair of tweezers, for removing splinters, etc.
Small 10 foot lock locking pocket tape measure (about $4 at Walmart) with a small super magnet (home depot, craft stores) epoxy glued to the end of it. Very handy for measuring things and retrieving stuff you dropped into in accessible places.
Small waterproof note book, pencil and inexpensive solar powered scientific calculator (keep the instruction manual with it, store both in zip lock bag) like the Casio ES115X at Wal Mart for $17, sometimes on sale for $12. In all my vehicles I keep these three things, except the tape measure there is a 35 footer.
The note book, pencil, calculator and tape measure, along with a bit of knowledge of basic Trigonometry, ratios and proportions will let you engineer your way out of a lot of sticky places, done that lots and lots of times.
A small battery powered radio, with extra batteries (that hopefully also fit your LED lights!) at least a general coverage AM/FM type, good for news and info (in certain circumstances you might have to take the news with a 100 bag of salt, can’t always trust it in a SHTF situation in this country , or any other), but my preference would be for a small hand held HAM radio like the Yaesu VX6 tri bander. Even with out a license, in an emergency you could use it to summon help, and the license is so easy to get, and only $15 , good for life (renew for free every 10 years is all) and that radio, and others like it , it also receives all the commercial AM and FM radio broadcasts, plus air traffic frequencies, , etc. It will receive all signals from 500 KHz up through 999 MHz, that includes all the short wave bands, air traffic control, commercial bands (that's police, fire, news station , taxis, etc. .
Good source of entertainment too , even if trapped somewhere, takes the mind off the bad possibilities.
Store anything you wouldn’t want to get wet , like TP, electronics, etc. in Zip Lock bags which can also be used for water and
food storage
The key to surviving any situation, if it is survivable, is to not let your mind get trapped inside the “disaster box”. Whatever has befallen you is a disaster if it isn’t your normal everyday pleasant life, so to get out of it as quickly and safely as possible, think outside the box.
Seek alternative uses for the objects you have with you or can acquire quickly even if it will destroy them, as long as the use they are put to frees you, saves you, etc. who cares, objects are replaceable, and even if they are not, you will still have the memories of them but you have to be alive to have even those.
Had to improvise, adapt, modify and overcome a lot of things in a lot of places over the 41 years total I gave Uncle Sammy, it got to be a habit very quickly to scan around me all the time and LOOK , not just see, what was handy should something get sprung on me in the next moment or two. Everyone with vision sees, but few learn to look, and then remember what they looked at.