Don't worry about piggies!
Slaughter is not involved. Pigs just give you some meat from time to time like wheat or seedlings do.

And about “RELAXED MODE”. In fact it's already embedded in the game in non-obvious way You can't loose. You can play level as long as you want and you will get bronze rating and some stars for upgrades anyway. And if you don't have enough stars to upgrade just replay level and get additional stars.

I have a major tip here:
Machines with fully loaded queue works 30% faster!

Also don't forget: upgraded trucks move faster. Sometimes it's crucial to upgrade your truck to receive gold rating (but sometimes not).
If you can't made it in gold time, maybe you just need to upgrade some recipes to “premium” (selling “premium” food gives you more money). Just play the game to the point where “Premium recipe” becomes available, upgrade and try the level again.