It's Not Like You're Digging a Ditch
If you come from a blue collar background, either your city town or family's work history, it's hard for you to work around people who aren't pulling their own weight. Your subconscious belief, college degree and all, believes that everyone should dig their own ditch. Well, the reality is it works better in your favor if everyone doesn't dig their own ditch.
The fact that we live in a "selfie, all about me, you don't exist, I need to be happy" world means, people like you stand out without even trying. Being a person who works to ensure every detail is taken care of and the job is complete when you walk away is not a bad thing. Those that don't have the same belief about work do the job the best they can, but aren't concerned with every detail and if they run into road blacks that means they are done. People who live by the "everyone digs a ditch" theory ensure that even if they run into a road black there is a continued attempt with the help of other resources if needed, until the original job is complete. This is like having a Golden Ticket to the promotion you've been trying to get.
The key to getting the promotion is to not complain about the people not digging, just keep digging your ditch. As your "ditch" gets deeper and is clean and precise those that need to notice will notice. Your first sign they are noticing will be when they ask you to pick up the job of the non-digger. Next thing you will look up and for the next project you will be tapped for the point of contact position. Depending on how that goes moves you to the next step.
Next time you are attempted to lose it on the person who doesn't seem to pull their weight, instead thank them for being themselves and being true to the stereotype of the new corporate worker. Their lack of concern means your "do a job well" workday will be noticed faster and get you out of the cubicle farm.