Looking for Champions

So my ping has been a thousand times worst than usual (okay more like twenty times, but +600 ping still hurts) and as such, my laning abilities are all but nonexistent atm. I've worked around this by falling back on my list of melee carries/raid bosses in the Jungle and playing "the objective game", swapping in for laners who need to restock items, resetting our waves whenever they are pushing towards the opponent's team, freezing enemy waves when they are pushing towards our towers, and in general being annoying and taking enemy towers via tele-splitpushing. So far it's been working quite well for making the best out of a terrible situation, but I wanna keep my options up so I don't get too bored of doing the same thing over and over while my internet's being...weird.

Basically, are there any Junglers that fit at least most of this criteria:

• Safe power farmer - won't starve or die too quickly in the Jungle (I have a trick to working around weak level 1-2 champions, so that's not the concern. I mean power farming any point after that).
• Good/safe wave clearer - Champions like Master Yi who can shove lanes with ease when the time calls, or those like Mundo or GP who can farm at a range and don't need to put themselves at risk while still taking advantage of minion gold.
• Solid splitpusher/tower threat - More or less self explanatory
• Low mechanical stress - Again, +600 ping. I can usually do simple tasks like ability canceling with Master Yi's Alpha Strike if I plan ahead, but there's no possible way I can, for example, insec people. The lower the skill floor, the better.