Just to chuck my 10¢ in, I've been using a FoodSaver for years. The "knock-off bags" work fine. I started buying them off of EBay, and my favourite seller then expanded to selling off of Amazon and Walmart's site. As I've commented elsewhere, they are 1/3 the price of Food Saver, making them less expensive than even FoodSaver's BOGO sales. I've successfully used all sizes (pint/quart/gallon) as well as the narrow and wide rolls.
So what happened to your machines? I've also been through a couple of them and replaced the seal on one (FoodSaver sells the foam seals.) I've found deals on refurbished on their site, when they've had them on the site. The 2 I bought at Goodwill should have been thrown out, not donated.