The general presser foot lift on a domestic machine is about 8 mm. On some you can push it a bit over seams and bumps and it will be fine (like a 201), others will have tension interefered with. I can push my 201 a bit more than my 99 if I remember correctly. You can search for a model with a high presser foot lift, also called high shank. They turn up now and then but aren't the most common. If you need the machine to hande 10 mm more than a few stiches, like over a seam or bump, you need a high shank.
For the Singer and Toyota models you mentioned, they will cope with hemming up jeans, but that is their limit. They maybe heavy duty compared to other low priced models, but they are regular domestic machines. I have seen both first hand, they are not the worst of budget machines, but their advantage is mostly buttonholer function and a few stretchy stitches.
If you can get by with a basic presser foot lift (low shank) take a look at an old cast iron model, something like a Singer 15 or 201, Pfaff 30 or 31, maybe a Husqvarna CB or a Jones will be up to the job. These straight stitchers are sturdy enough to handle webbing and dog collars, and they turn up at a good price.
Janome have some Easy Jeans models like 22 and 1800, and they have a higher presser foot lift. These two are very similar and relatively sturdy models, but they are still nothing like a cast iron straight stitcher. A new machine cost a bit more, and are still within the basic sewing machine range.
For something more than that you have too look at an industrial model with high presser foot lift. Most used industrial machines that turn up around here have the basic low presser foot lift of around 8 mm.