Okay... just my two cents now... pure rhetoric... you might think about it...
The embassies and consulates are under the authority of the Foreign Ministry, immigration is part of the police. Means, in principle they are two more or less independent authorities. So... now you could assume that the employee in the embassy is not really interested in what you (may have) done here, but of course you can't rule it out.
Personally, I would try not to give them any reason to think too much about the start of the contract and my entry and so on. Remember the tiger...? 😉
So if you assume that the employee in the embassy might find something strange, re-dating the contract would be the best option here... as close as possible to the date of the visa application.
Nah... I wouldn't do that... it implies that you are working (from) here already and that you know that it is actually illegal.
There is no need to "formalize" your stay if you are just a tourist. So... does your paperwork show in any way that you are "on duty" already for this company from here? If not... Never wake a sleeping tiger... 😉