There are likely a lot of values of the form 0x713xxxxx -- 2.6 MB might be larger than you've thought when you start looking through it more or less at random (you don't actually know that the application uses this date format internally).
The conventional approach to deal with this sort of problem is to use a tool to step through the program, examining the code that is executing, until you find the point where the check occurs. Then simply disable the check so that it always fails -- by altering the date, or simply by altering the code.
A popular tool for stepping through code that you do not control is the Interactive Dissassembler, IDA. You can download a freeware version of it here: https://www.hex-rays.com/products/ida/support/download_freeware.shtml
It might be harder than you think to do what you want, but you'll almost certainly learn a lot by trying.
Be aware of the legal issues you may be getting yourself into by making modifications to someone else's binaries, particularly if you distribute them afterwards.