So after some trial and error and process of elimination I found that removing the Elemental Creepers mod "solves" this problem.
However I ran another server 2 or 3 years ago using nearly identical mods to the ones I'm using now (including Elemental Creepers) and never had this issue. The only difference now is I'm using newer versions of the same mods I had before (assuming newer versions were available and that they're not alpha or beta releases).
So this makes me think that Elemental Creepers itself isn't necessarily the problem but rather another mod that got updated is as I'm using the same version of Elemental Creepers now as I was a few years ago on my prior server. I would imagine Elemental Creepers is a fairly simple mod in and of itself so some other mod that got updated is probably not playing well with it.
Knowing that removing Elemental Creepers stops my server from crashing, is there any information in either of the 4 crash logs I posted that would now shed more light on the issue?
If it's not another mod causing the conflict, could it be Forge itself? Apart from having some newer versions of mods on this server, the only other difference between this server and my last is that I'm using a slightly newer version of Forge as well.
I'm not adamant about keeping Elemental Creepers. If I have to get rid of it then so be it. I simply like it because it adds more variety of mobs to face. I'm sure I can find another mod that adds more mobs to replace it though.