A syringe is a great idea. Spending $600 to $900 for a machine isn't in my budget right now, but I would definitely do the math. Guesstimate how much you can sell, and how long it will take you to fill the straws by hand, and then compare that with the machine cost. Time really is money, and you may be able to make up for it in a short amount of time.
If doing it by hand, I'd fill up the longest straws available, or within reason, get a stack of them, then heat seal in segments of whatever desired length, and as fast as you can. That is why I'd have to agree that a heated injector or modified syringe would work very well to save time. You don't want to be filling a syringe every straw or two.