I was about to say just take a fire resistance potion and forget the lava risk but the obvious fact I almost overlooked is that those won't be available before the first time before you enter the nether.
I'm also surprised at the stone tools for the first trip into the nether but maybe that was a conscious choice to minimize loss? I still would have at least brought iron though. Mining out in stone would be more painful. Honestly if faced with that sort of situation I'd definitely go back and bring the diamond one (if it still exists).
I finally found a fortress, obtained only 3 blaze rods and discovered an archipelago of large mushroom islands.
I had one fire resistance potion from piglin bartering while bridging across the Nether at an altitude of approximately level 110. Just before reaching the fortress, however, a ghast very unfortunately had to inform me of its arrival and started shooting fireballs, and because of its angle to the bridge it was rather difficult to reflect the fireballs at the ghast.
After the ghast shot 6-7 fireballs, a lag caused one fireball to appear later than it actually did, and I got knocked into the lava sea below, with almost no land in sight. It's probably because I didn't know how to use splash potions at the time, because when I quickly swiped the fire resistance potion from the inventory and used it, I obtained 40 seconds of fire resistance instead of what was according to the item name 3 minutes, and so I obviously did not make it onto land in time.
After this first death, there were many magma cubes blocking the way on the bridge. Some simply jumped off, some required killing, but sadly no magma cream was obtained. I finally finished bridging when a piglin spawned on it, and at the same time the blazes below were starting to shoot fireballs, knocking the innocent creature into the lava sea far below.
Since water doesn't work in the Nether and I had no easy access to a snowy biome from my survival island, I could only use honey blocks as a clutch method. Cobwebs are harder to obtain and I mainly use hay bales as a farming ingredient.
After missing the clutch and dying for the second time, I made another attempt and was successful. However, I had not noticed the mass of wither skeletons crowding around the area of landing.
After dying for the third time, I killed a couple more magma cubes on the way to the fortress. When I arrived, the wither skeletons have gone, but I forgot to bring a fire resistance potion and five blazes appeared out of the blue and started shooting from different directions, causing shieldwork to be challenging, and I died.
On my way to the fortress, I missed the clutch and died again.
Finally, I killed several skeletons and blazes, most of which did not drop any rods, though in the end I obtained 3. There was a particular incident on one of the narrow bridges where two blazes spawned close by and I discovered that they shot fireballs simultaneously and at long intervals, like pillagers, so timing of attacks were relatively straightforward. I was about to go on locating more blazes when the subtitle "Ghast shoots" appeared, and I immediately went into the cover of the fortress to avoid the explosion induced by my least favorite mob.
There, I built a temporary shelter and an emergency portal to the Overworld. At first, I was quite relieved to escape the hellish dimension, but then I spawned in a cave deep underground at level -14. I quickly built a wooden shelter, since I was out of blocks like cobblestone or basalt. After ensuring that the shelter was secure, I started mining up to escape the cave, something I have never had to do, and had no idea how far I was from my island. Luckily, I had brought my compass in case of such emergencies, and this qualified as a definite emergency. While mining up, I was forced to mine various underground blocks that would clutter up my inventory, such as coal, iron. diorite, andesite and gravel. I didn't bring enough torches, so I had to use my flint and steel as a temporary lighter. I finally mined the outer gravel layer and burst into the ocean, where I discovered a massive mushroom island close by. It was time for the long journey back to base.
I can only imagine a "yay, I'm out of the nether!" to walk out of a portal into pitch darkness, hearing a funny sounding cute thing, followed by a noise of terror, and panic as everything gets dark. At least that didn't happen.