I always stay on top of prices in my industry so I have a good idea where things, salaries, contracts, etc, should fall. Sounds like your gut is telling you your price and I'd go with that even if I thought they could pay more. Maybe they can and maybe they can't. However, I've found when I go with my gut on pricing, the deal is more likely to go through (although it sounds like you're pretty firmly in the signing territory already).
I think about it like cashing in on stocks or options: there's always more juice to squeeze but if I'm happy with the transaction, I'm happy and I don't think about it anymore. You can always wonder without end if there's more to be had.
Personally I also like to feel like I've been fair even with the chance of pushing the limit with a corporation. It's more about my integrity than their pocketbook (and just because they're grifters doesn't mean I want to feel like one myself by over-charging).
Still...have you sold to a company of this size or revenue before? Might want to look more into deals exactly like this one if you think you're leaving anything on the table.
I would be worried if you think it's a risk to your business. How great would you say the risk is and at what impact? If a greater risk, enough to cause any downswing in business thrust over a year, I would skip the deal. Rarely is a deal worth the risk of tipping your scale in the wrong direction, not just for money anyway (though I've done it to enter new markets or "project some muscle"). If a smaller risk, more of a inconvenience, I'd not let it affect my decision.
Hope some of this helps, brother. Definitely want to hear how this goes and what you decide.