I'm not 100% sure about the meaning of the source phrase, but "the early bird gets the one" could be one option in English. This saying is typically used to congratulate proactivity and getting work done early in the day. Used by a boss to refer to himself as one "early bird" among others (his team) this would imply that he is seeking positive results for his operation by being active in the daily work.

"No rest for the wicked" is a very common idiom in English that might work here. In this context, the owner would be saying that he is obliged --almost supernaturally-- to work constantly because of his previous shortcomings (a.k.a. "sins" as implied by the religious metaphor). This would be an example of dry humour, with the owner basically saying he is compelled to work because of his "sin" of being an entrepreneur.

Here the boss would be implying that he is pushing for a positive result (the spoils) by working alongside his employees and providing an outstanding active presence (the victor). The saying also implies the competitive nature of business (i.e. the boss is willing to be a positive role model for his team by outperforming them).

all hands on deck

The idea, as the OP mentions, is that the person responsible for the business should be the one working the hardest.

The English saying "lead from the front" means that the leader should take the initiative and set an example in order to inspire his or her followers (employees, soldiers, etc.) to work their hardest. I think it's appropriate in this context since the scene OP describes is the business owner hustling to get his crew ready.

What this translation is missing, however, is the self-effacement present in the original Portuguese, where the owner is referring to his business as a cadaver of which he, being responsible for said cadaver, has to carry by the head. The English phrase is pretty self-aggrandizing, and anyone who says it about themselves might be the subject of some eye-rolling. It's also a bit militaristic, in the sense of 'leading from the front lines'. However, it could work for a subtitle where the goal is to get a common idea across quickly and effectively.

References:

On "dono de defunto"
http://www.fernandoguifer.com.br/index.php/2017/02/23/tua-vi...
Apesar disso, deve-se haver cuidado em não transferir as responsabilidades para um alguém que não carrega autoridade suficiente para bater o martelo.
Este papel é teu. Incompetência não deve ser terceirizada e o dono do defunto deve pegar sempre na cabeça.

For "lead from the front"
https://idioms.thefreedictionary.com/lead from the front
lead from the ˈfront: take an active part in what you are telling or persuading others to do: If you want to succeed in this business, you need to lead from the front. We need people who can motivate their team to get the best possible results.

https://www.lexico.com/definition/lead_from_the_front
Lead from the front: Take an active role in what one is urging and directing others to do. ‘in his two appearances as captain, he led from the front’