Your current company has a lot going for it.
You're happy where you are. That won't happen everywhere. You're well paid. you might not be paid as well elsewhere. You get to learn and do a lot of things that others in your field don't (and that you might not be able to once you leave). Those are significant motivating factors.
Your current position is one you've lovingly crafted for yourself over a long period of time.
You've said that you're the only engineer at your company qualified to do the things you do. That means that you're the only one qualified to make decisions on tools, techniques, standards, and whatnot. All of the little decisions that engineers argue over in larger companies have been yours and yours alone. That can have a large effect on your personal comfort level with the work.
Working for your current company is inherently risky.
They've missed payroll in the past. That's a big ugly sign. They've always payed it back afterwards, which is good - it means that it's a matter of cash flow, rather than a matter of trying to exploit you. The issue is that companies who miss payroll sometimes fail entirely, and if it fails entirely, there wont' be anyone left to give you your back pay. Money is oxygen in the corporate world, and your current company is fighting desperately to get enough to breathe.
If you don't bail now, it's time to start thinking about when you would bail. Would it be after your pay was a month overdue? Two? Basically, if you're going to try to stick it out with these people, you need an emergency fund. Budget it to cover for however long you're willing to let them keep you in arrears before you bail, plus how long you think it would take you to get another job. It doesn't have to give you everything you'd normally buy for yourself when flush with cash, but it does have to be enough to live on. Admittedly, an Emergency fund is worth having regardless. It's especially worth having if you're workign for someone who might not be able to pay you.
Right now, this moment, you have a chance to escape the risk. The question is whether you go for it.
You will almost certainly not like the new job as well as you like this job. You will be forced to adopt practices you disagree with. You will be required to submit to bosses who don't give you as much control as your current bosses. The atmosphere will be different, and you won't have nearly as much access to upper management. Also, you won't be as critically important to the livelihood of everyone you interact with on a daily basis. Maybe these things are important to you. Maybe they are not. You're the only one who can decide whether the financial assurance you'd be getting is worth the carefully cultivated work environment you'd be leaving.
Your current company could recover entirely. It could collapse two months from now. It's a gamble. It's up to you whether or not that gamble is worth it, and how many times you're willing to raise before you fold.