Big lag on mp with similar specs

[Asekhan]

My friend and I have been playing for a while on a modded game, as the game is not very multi threaded I run the server independently on my own machine so he can connect when I'm not there. Everything was all good for a while, until we hit the point where the server cannot keep up 60ups (100+ hrs with mods). As I run server and instance on the same machine, most of the time it's fine, but if I do anything that take some processing power, like opening a big inventory (viewtopic.php?f=183&t=35318) or simply opening the processing screen. My instance take more time per frame, not enough to actually get dropped, but enough that I can't move, the ups drop to 5, and any action I try to take take forever to be taken in consideration (and I apparently need the server confirmation to close the damned windows, so I get stuck in the production screen forever).

Now if I play in single player or host myself, I don't have any issue, but still, my friend has a very similar computer (i5 3570k instead of my OC i5 2500k) and he have the exact same behaviour upon connecting to me.

So my question, is there any way to actually make the server slow down when the connected player can't keep up?
Also, is there anyway to disable the damned catching up phase on connection? I REALLY prefer the server to pause for 10 seconds for the download instead of waiting 5 minutes to catch up (as the specs are too close it take forever to catch up)

Is our only solution would be to actually get a worse computer and run the server there instead? That's counter intuitive and we would lose general performance to fix the horrible lag spike, aside from the fact that I would actually need another computer....

Is there any other solution I would have overseen?

My specs for reference but I don't think it's relevant :

CPU : i5 2500k
RAM : 24Gb
GPU : GTX 1070 8Gb

I could upload screenshot of the debug mode, but again everything get scaled up and nothing is the sole cause of the lag, it's like it was multiple tiny catch up in a row.

[impetus maximus]

you could try limiting the threads for the server (config file) and your client to 2 threads each.
then change the affinity for each instance to run on seperate cores. server on core 0 & 1, client on 2 & 3 for example.

that's what i do on my server.