Is there a relatively easy and efficient way to spawnproof large areas in the Nether?

Minecraft 1.13.1, Java Edition, survival single player.

I'm in need of a beacon or two, so I'm trying to build a Nether Fortress farm based on Tango Tek's design. Following his directions, I found a Nether Fortress over a lava lake where I built the farm in survival mode. However, the rates I was getting were miserable, no better than just wandering around the Nether Fortress as I found it.

I loaded a copy of the world in creative mode and found out where all the mobs were spawning using a command block to continuously apply the glowing effect to all entities. It turns out that there were plenty of spawnable blocks within a 128 block radius around the farm, and so pigmen were spawning liberally in these areas and filling up the mob cap. Generally speaking, there were two areas where the pigmen were spawning: the nooks and crannies in the nether ceiling below the bedrock, and the shores of the lava lake, which despite looking far away, were actually rather less than 128 blocks away from the edges of the farm. Of course I could (in theory) find a different Nether Fortress on a larger lava lake, but it already took quite some time to find this first one, and regardless the Nether ceiling will always be a concern, since the Nether is only 128 blocks high. So one way or another, to improve the rates of my farm, I need to spawnproof large areas.

Spawnproofing large areas in the Overworld is quite easy with an inventory full of torches and a little bit of cave exploration, but I haven't found the same to be true for the Nether. Torches aren't an option, since pigmen and ghasts spawn at any light level. Another common approach, flooding an area with water, doesn't work in the Nether either, since water can't be placed in the Nether. So I tried a few other things.

My first approach was to mine out as many blocks as I could from around the farm, since an Efficiency V pickaxe insta-mines Netherrack and Magma blocks. It quickly became apparent that this would be incredibly tedious despite the insta-mining, and also this doesn't solve the problem of the lava lake shores. My second approach was to flood exposed ground in lava, similar to the water flooding approach for the End or Overworld. I quickly ran into a couple problems with this approach: unlike with water, it's impossible to make an infinite lava source; and lava is quite dangerous, even with fire protection enchanted armor. My third approach was to place slabs on all exposed areas, but like the instamining, it soon grew very tedious, and I had hardly even made a dent in the 128 block radius around the farm. Based on the 15 or 20 minutes I spent placing slabs, I figured it would've taken at the very least 5 or 6 hours just to spawnproof with slabs, which seemed like way too much, since I had already grown bored and glassy-eyed after just those 20 minutes. Even using cheats - the fill command specifically - I couldn't find a way to easily spawnproof the region around the farm, since fill has a limit on the number of blocks it can place with a single command, and so I would've had to run hundreds of fills to completely remove all blocks in a radius around the farm.

Is there a better way to spawnproof a large area in the Nether (e.g. for the purposes of improving the rates of a Nether Fortress farm)? Ideally something that would take just an hour or two of work in survival? Or should I just suck it up and spend all day placing slabs?

Just one last note - since all Nether Fortress farms depend upon the same spawning mechanics, I would imagine that the ideal conditions for a Nether Fortress farm would be the same regardless of the specific design of the farm itself, so I assume that this question would be equally relevant to any Nether Fortress farm design.

Annoyingly, the best solution is slabs.

I've dealt with this situation before with a friend of mine. over the course of a few days of mining and placing, we slabbed a huge area of the map.

The second best solution would be to put the farm above the bedrock ceiling.

1. Punch a hole through the ceiling (dragon egg).
2. The nether fortress is defined in certain chunks. Find these chunks, and build the farm in the fortress chunk.
3. Make an AFK point at world height, with some form of fast-transport system to the bottom of the farm (bedrock "ceiling").
4. Profit from lack of mobs, besides in the farm.

Also, I do not know what design you're using, so it may not work.