Never in my entire life have I encountered the NEED for a turf blanket. Fall is the BESTUS time for getting lawns to be established before the spring. The fact that you are close to maritime influence means even better temperatures. Seed might be a bit late for germination but I've been in far tougher climates and at this time of year those that wanted to seed we talked them into using a grass spray seed company. They include a mulch to not only keep baby seedlings moist but to protect them from a bit of frost.
I'd wait for spring to try again or I'd go see if sod was available/viable for the locale. Hand seeding has NEVER made a beautiful lawn in my experience. Well, I've done it but it took constant supervision over the owners and baby grass and I did not live next door nor was I paid for my time. Seriously. Either professional grass seeding or sod. The difference in price is negligible and completely worth the extra pennies. I learned quickly how to educate people who wanted a beautiful lawn who only wanted to pay for manual seeding?! Screw that, I needed to have success. It was always my responsibility and if I had to make a lawn by spreading seed manually I said, 'go find someone else'. Lawn blanky...new one for me, just can not see the value at all. Nope, not at all. How many square feet is this lawn? Do you have an edge created yet? Is it rolled and graded and rolled again? What kind of seed has been used? I only used Professional's Choice with zero weed seed in the Pacific Northwest. Using seed from Lowes or Home Depot just means one will have to redo the entire thing all over again. Not a great position to be in Idiot!! Grins! BTW, your clients can afford to do their lawn correctly. This is like Rumpelstilsken making that gal with long hair spin gold from straw. They expect you to perform with substandard conditions and perform or else YOU will have to pay for their lawn. Why the hell would they stop you from seeding earlier, because they weren't THERE? Oh my, we need to talk.