Holy crap, I guess all I needed to do was complain in the thread. After a bunch of frustrating games tonight, only getting in the top 20-30 maybe once, I got my first ever win. Like everyone says, it's really heart-pounding. I shall tell the story with screenshots. Please forgive the massive wall of text, since I'm super happy I finally won.
The night was frustrating because I was attempting to drop in heavy areas and practice shooting. I'd either not find anyone, or find maybe one player and then die abruptly. I'd try to shoot an automatic weapon and die to a pan headshot. I got a pan kill in one game, and a shotgun kill in another, but not much else.
Persistent Jerk
Then, it became frustrating because I'd start running into persistently mean people. Let me illustrate. I'm minding my own business, I have awful weapons (double barrel and pistol, possibly), and my only hope is to drive a boat around the military island and find an uncamped house. That's when I notice a crate. Huh, never seen one drop in that spot.
I kept being paranoid and scouting for boats. I shouldn't have, because even that slight delay resulted in someone cruising across the water to the middle of nowhere, just for the crate. It had what I think was my first ever ghillie suit. It also had a tommygun I didn't even have time to load before I started being sniped.
I didn't think you could easily see someone on the bottom of the ocean if you're driving a boat, but somehow this jerk could. I'd circle the crate. I'd circle the boat. I'd swim far away. I'd swim under his boat. No matter how deep or how far I swam, he always seemed to be able to see me while still sitting in the boat (maybe there's a third-person trick I don't know about?). This went on for probably 3-4 minutes -- back and forth, in circles, way outside the safe zone, disregarding his own positioning just to make sure he killed me. In the end, I tried to suddenly hop in my own boat and start driving, but I was instantly headshot with a sniper rifle from close range.
The Walking Loot Box; Pondering Suicide
Eventually I ended up in a game where I was dropping into the military base. I missed all the buildings and ran up to the roof, No weapons of course, but I found an 8x scope. I instantly decided that scope was worth the entire military base and raced for the ground and the hills. Of course, no sooner had I started driving a jeep away from the base, some jerk started shooting at me. Because yes, of course the naked lady with no weapons probably has great loot, and it's worthwhile to attempt sniping her jeep.
I looked at a couple of other spots on the island but everywhere seemed to already have been looted, so I ended up on the mainland. I feel I've seen basically everywhere but I don't remember exploring the particular coastal village I ended up in. I managed to get nice helmet/vest/backpack stuff, maybe a pistol, and a single grenade. I had ammo, a few health items, and both a 2x and 8x scope. I got a level 3 helmet of all things, just sitting in a garage. I felt useless to myself, but practically a walking loot box to anyone else. I pondered whether the proper answer was to kill myself so far away from the playing field that no one could loot my scopes and armor. Then the situation finally improved. Village houses had both a Kar98 and an AK47, so those got my scopes.
Persistent Jerk 2.0
I was paranoid trying to push through the village as the circle shrank, but healing items kept me from taking too much damage as I got back in safety. I think I was stuck to the west of the west military bridge and needed to get east, but I saw a red zone and I still hold to the belief that red zones mean someone is there. There didn't seem to be cover, so I finally ran for a road near the wall, gambling a car was my best chance. I did indeed find a Dacia, and started trying to get a safer spot somewhere in the middle.
This is when I ran into another persistent jerk. I was merrily driving along through hills and such, and someone started trying to snipe me out of the Dacia. I wasn't even going that slow! I got down to maybe 1 tick of health, managed to juke to the passenger seat to avoid the death blow, and then back to the driver seat to try to get to the bottom of a hill somewhere. I used a medkit, got in the car...soon started getting sniped again. I started driving super far away, around a hill etc. Still being sniped. Maybe they were on top of a really tall hill, but wherever they were it took quite a while to get completely out of sight.
The circle is pretty small and everyone can hear the car, so I figure my best chance is just to speed up to a 2-story building and either rush it or shelter near it. Maybe 15-ish people alive, and the door is shut so obviously someone's there. I opened it from the side and someone immediately started spraying tommygun or M249 shots through. OK, I'm awful with grenades but I tried the one grenade I'd found, a frag grenade. Nothing. The person in the building starts throwing smoke. I circle the whole building, surprised no one else has tried shooting me in the mess, and eventually I just prone on the outside edge trying to cover that escape route. Turns out the building person had a motorbike on the opposite side and drove off, which was fine by me.
The End
By this point the circle was getting really tiny. There was almost constant fire from 2 or 3 parties who were apparently having a long-distant gunfight. I had pretty high health, proned my way near the circle, and shockingly no one had shot at me yet.
Notice how close the blue circle is. At this point I promptly almost choked, because I was terrified to crouch or stand up and I waited too long with the blue circle. I had literally 1 tick left when I reached the white again, and EmCeeGramr's dire stories about circle tick lag were ringing in my ears. I don't know if I had any healing items left at all. The gunfire was still going. If you look at the screenshot, it sounded like one person was on the top left hill, which should be impossible because that was outside the zone. They could have been on the lower left, where a boat was beached. Then there were 1-2 people in front of me and to the right, apparently firing back and forth at the others. I couldn't see anyone at all even with the 8x scope.
I was terrified to switch weapons because I thought the animation might go up in the air and reveal me. I tried it; it didn't. I went back to the sniper rifle. I got far enough to check out the boat, and didn't see anyone. Still with my 1 tick of health, I suddenly realized there were only 2 left in the game, which really kicked in the adrenaline. I think the other person shot randomly once or twice so I still hadn't been spotted. I moved forward a little more and realized they're ahead of me, next to the tree, looking SIDEWAYS.
I tried a single Kar98 shot, and it was a headshot kill through a level 3 helmet. That's probably my only Kar98 kill ever, and my only 8x scope kill ever. It was my only kill of the game. It turns out ditching the base with nothing but an 8x was the correct choice.
And so I got my first ever win, in solo mode, after 56 hours played. Thanks to those who gave me tips.