Rammus is a tank as much as the other two, and Nautilus' contribution is ganks too. Their ability to jungle is too weak.
I want to focus on how to make them able to jungle, since a tank should be contributing ganks more than not.
Mana gate sustain is an issue on its own as is health sustain.
Because junglers (or even tank junglers) that rely on using abilities consistently with their mana need a way to help teeter the mana pool a little better.
I don't have an example for this one but for a jungler that doesn't use their abilties to clear the jungle mainly, then they have to tackle their health sustain issue.
So since we have this new enchantment pseudo create your own item for the jungle item, what if the enchantment tree extended larger in its building paths?
I'm not talking about trail blazer (among 4 first paths) into devourer (among the tier 2 paths of four other enchantments) to become an entire whole item.
I mean, what about a type of slotted enchantments that the player can pick up in the form of passive and/or small stats?
example: I buy rangers trail blazer, then I can pick an enchantment of my choosing like say "Damage received from/dealt to monsters is converted to mana" for a cheapy price of like a 100g?
Cause it is supposed to only be paying for an additional passive.
And it can be brought both ways, before final enchantments like purchasing devourer or before you make that tier 2 jungle item.
Then later as time goes on and I get the gold, since early clearing wasn't as painful I can still get my tier two enchantment jungle item finished with my passive perk I chose.
This could be candidate for letting players pick old spirit stone sustain passive, quill coat thorny mail, quill coat's/wriggles/ancient golem's ward active and maybe even other experimental perks directed at early jungler issues that players can further tailor to their playstyle and jungler of choice.
EDIT:
basically, the new jungle items alter the function of how smite works and come with a passive.
Perk Enchantments can be bought and still stay along for the ride as they function as a means of tailoring the function of how your clearing problems are affecting you.