We're on version 0.2.41 of ATM7. We were fine for a while, then started getting one of these errors ever hour or so and now it's constantly to the point where we can't play. I can't find much helpful information on the internet but I did try (in vain) some fixes I saw around such as:

-downgrading forge
-changing modpack version
-restarting both PCs
-restarting the network
-removing certain modded blocks from the area such as Create machines and Refined Storage blocks
-removing mob grinding utils cause some guy on a forum said that fixed it (desperation)
-disabled firewall on both PCs temporarily (desperation)

Also, digging through the logs a bit, I believe this here is the relevant section (whenever she joins there's four errors and then the disconnect):

[18:34:52] [Server thread/INFO]: Using new advancement loading for net.minecraft.server.PlayerAdvancements@603a99c8
[18:34:52] [Server thread/INFO]: PLAYER2[/192.168.1.21:62638] logged in with entity id 35514 at (1084.8722414068873, 69.0, 442.3451810586436)
[18:34:52] [Server thread/INFO]: Sending ToolHandleTypeManager to PLAYER2
[18:34:52] [Server thread/INFO]: Sending SnowcapOvenFreezingManager to PLAYER2
[18:34:52] [Server thread/INFO]: Sending HorizoniteForgeFuelManager to PLAYER2
[18:34:52] [Server thread/INFO]: Sending AlchemyRecipeManager to PLAYER2
[18:34:52] [Server thread/INFO]: Sending JournalEntryManager to PLAYER2
[18:34:52] [Server thread/INFO]: Sending JournalSectionManager to PLAYER2
[18:34:52] [Server thread/INFO]: Sending JournalRequirementManager to PLAYER2
[18:34:52] [Server thread/INFO]: PLAYER2 joined the game
[18:34:52] [Render thread/INFO]: [CHAT] PLAYER2 joined the game
[18:34:52] [Netty Server IO #7/ERROR]: Could not serialize cpw.mods.inventorysorter.InventorySorterCommand$ContainerClassArgument@6222743b (class cpw.mods.inventorysorter.InventorySorterCommand$ContainerClassArgument) - will not be sent to client!
[18:34:52] [Netty Server IO #7/ERROR]: Could not serialize cpw.mods.inventorysorter.InventorySorterCommand$ContainerClassArgument@d8b6f37 (class cpw.mods.inventorysorter.InventorySorterCommand$ContainerClassArgument) - will not be sent to client!
[18:34:53] [Netty Server IO #7/ERROR]: Could not serialize cpw.mods.inventorysorter.InventorySorterCommand$ContainerClassArgument@6222743b (class cpw.mods.inventorysorter.InventorySorterCommand$ContainerClassArgument) - will not be sent to client!
[18:34:53] [Netty Server IO #7/ERROR]: Could not serialize cpw.mods.inventorysorter.InventorySorterCommand$ContainerClassArgument@d8b6f37 (class cpw.mods.inventorysorter.InventorySorterCommand$ContainerClassArgument) - will not be sent to client!
[18:34:54] [Server thread/INFO]: PLAYER1: Set own game mode to Survival Mode]
[18:34:54] [Render thread/INFO]: [CHAT] Set own game mode to Survival Mode
[18:35:05] [Server thread/INFO]: PLAYER2 lost connection: Disconnected
[18:35:05] [Server thread/INFO]: PLAYER2 left the game
[18:35:05] [Render thread/INFO]: [CHAT] PLAYER2 left the game

Unfortunately, I don't really have the RAM to just do the whole dedicated server deal, so any info on how to fix this would be much appreciated. I was hoping LAN would be quick and easy...

I get both the inventory sorter ERRORs as well as the INFOs when I connect to my dedi from inside LAN but I am still able to connect. You should try 0.2.42 as 0.2.41 included some parts with performance issues.
Edit: actually just 13s for join to disconnect seems too fast for perf issue. But 0.2.42 is worth a shot anyway

Same issue for me.

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