Part 2
Even if Shaco and Mundo have your top outer turret, you can take their bot lane second tier. Keep good ward coverage around you (don't want Fiddlesticks jumping out on you) and you have complete control of Shaco's red side. Keep pushing your map advantage, shove towards mid second tier, and basically the entire jungle is yours. You can take top outer tier easily (if Ryze hasn't already taken it) and just take top second tier, take dragon when it's up. and the entire map is yours.
General themes are out rotation and map control; you don't want to head to head siege vs. Ziggs, but if my hunch about his playstyle based on summoner spell choice is correct, rotating around the map forces him to respond, pushing him outside his comfort zone. Shaco has great map control because he has his boxes and his mobility and stealth; you have to beat him at this game, keep track of him in the jungle, out rotate him and take objectives. Map control and good warding is vital vs. Shaco, even more so vs. Shaco and Fiddlesticks. If they make a play somewhere on the map, make a bigger play somewhere else, take an objective, take dragon, turrets, whatever. You can work around picks, but like you said, your teamfight is weaker than theirs. Shaco on the other hand works great at picking people off, so move as a team and he'll have a hard time; you don't want him to ambush you when his team is ready to fight, it just causes too much chaos.
If you can push them to their base, push all their lanes to their base. Ziggs and Jinx have great waveclear, if you only have one lane pushing their base they'll just clear it and you'll have nothing to do. If you have all lanes pushing their base, they can only handle two of them; take the third. Even if Ziggs clears that wave with ult, his ult is two minutes; minions spawn every thirty seconds. If you can keep bot shoving, someone will have to deal with that, which means you can force around Baron. You might not want to actually do Baron, though, unless they're not responding. If you can get a pick, that's good, go back to pushing your lanes. If you get a pick on Shaco, you can probably do Baron if your lanes are pushed and no one else is coming to respond (if they are, you can zone and run interference). If you divide up their team, so only one person is defending an inhib turret, you can probably dive them if Xin is tanky enough. If Mundo is sent to handle the split push or clear a different wave, that's fine, they now have no tank at all. You can Ult+E Xin when he dives for massive AoE damage and a shield. Nami has CC which can really help turn a 4v4 teamfight in your favor. Ideally you take them when you have the numbers advantage, take turret, maybe inhib if you have time, and back out; take neutral objectives (dragon, maybe Baron if you can manage it), base and repeat; you now have one wave auto pushing in your favor (preferably a side wave, since it'll spread them out more). Go pressure your other waves, keep good ward coverage so Shaco/Fiddle can't sneak up on you. The advantage you have is that Karma works incredibly well for helping teammates rotate to objectives because of Ult+E. If Ziggs and Jinx are guarding one turret, go pressure the other, and if they're each guarding one, you can dive one of them and take that turret. Keep pressing your advantage methodically and win the game
The nitty gritty stuff I'm not too great on, but essentially, you want to split their team up, while keeping yours grouped and keeping pressure all around the map. It's difficult vs double teleport and a Ziggs, but it's the best option I can think of. Out rotate them and take control of the map.
"Fight the enemy where they are not" - Sun Tzu