I've never seen a product that could help but hopefully our readers will have some good tips for you. 

I do this too. I have found that when I've had too much caffeine my hands are less steady. So, think about if you are under the influence of caffeine, or alcohol or any other drug for that matter. I have to watch out for soft drinks and energy drinks.

I've been doing my own nails for 35 years (that's a lot of fume inhalations!) and I definitely have gotten better with practice. I guess if you wanted to practice a lot you could use a plastic hand that beauticians use for practicing when they are in school.

Something I read a while ago that I think could work: Olympic target shooters hold their breath when they fire, because your hands are steadier when you are  holding your breath. So, maybe if you hold your breath when you are brushing on the polish, your hand would be steadier?

It just takes practice. Place both hands on a table; even the one you're painting with. Don't lift that one up completely because it will shake. Also, try and use as few strokes as possible because otherwise it starts to get messy and lumpy. When you're putting down your first stroke, don't place it right at your cuticle because that will make it look sloppy since we don't want polish ON the cuticle, just right up to it, so place it about 1/8" before your cuticle and carefully push the brush up towards the cuticle without actually touching it. Do the same on the sides. Getting polish down in that crack on the side of your nail looks super sloppy. If you can avoid the cuticle and sides, your manicure will look great. Also, I find that when people wipe too much polish off of the brush before applying it, it looks sloppy and uneven. Only swipe off one side of the brush and leave the other one alone. When you get to your pinkies you'll want to swipe off a little bit of the side that you normally leave alone since this nail is much smaller than the rest. Let me know if this helped at all!

practice, practice, practice

That is a very interesting tool but I don't think it's long enough on the sides, but anything is better than nothing. You could also use a piece of scotch tape on either side of the nail.