Hi again, Mark, and thanks for your additional and helpful detailed information.
I think there may be a more direct way for you to go, and from your initial information, plugging in 'Hackensack' as your starting point, to New Hyde Park as your end point, I got this information:
You can go to the site and change your leaving point to Maywood and see if/how it changes, however, there's no change in that you'll need to take the New Jersey Tpke to the GWB to the Throggs Neck Bridge, to the Cross Island Pkway, and that might be a more direct route for you.
If you don't already have one, get an EZ-Pass from the New Jersey Tpke Authority, and this will discount your tolls. You might need to purchase a different EZ-pass for the NY tolls, like on the Throggs Neck Bridge. I believe there is no toll on the Cross Island Pkway. If you can at all, avoid the LIE (Long Is. Expressway).
According to the info at the site above, the trip should take an estimated 43 minutes, but I think that is conservative, especially in rush hour. Total travel time is 27.24 miles.
In my personal opinion, unless you don't mind the driving, this particular job is offering you a great salary, benefits, etc., it's something you will love doing, and you would really like to consider it, plus, if you're currently not working and you've been looking for a job for a long while and have gotten no offers, it might be a good idea to consider accepting this offer. However, if there is any way you could get a comparable job closer to home or even in the City, to which you could take a PATH train, express bus, etc., weigh whether the travel time, expenses, etc. are worth the salary, benefits, etc. Also, keep in mind that traveling to and from, in rush hour, is going to be crowded, and remember in the winter, with bad weather, snow, ice, etc., it will be slower.
If you'd like to experiment and try this other route, see how it goes. Also, if you have a GPS or a friend does, you might plug in your beginning and ending addresses, and get travel directions from there, plus a total travel time. If you don't currently have one, it might be a good investment, especially if you will be traveling far from home to an area you're not very familiar with, and if you should have to take a detour, etc., it can help you with alternate routes. The prices have come down tremendously, and you can even check on eBay.
I wish you much good luck, Mark, whatever you decide, and hope everything works out great for you!