How do I keep embroidered letters from looking wobbly?

The shaky lines are almost certainly coming from stitch length, not from how you were sitting. On curves, backstitch needs to be much shorter than people instinctively make it. Long stitches on a curve force the line to wander to one side or the other, and that's what reads as thick and thin. Aim for stitches no longer than a grain of rice on text, even shorter on tight curves, and always bring the needle up or down right on your guideline, never beside it. If the guideline itself was wobbly, you're stitching a wobbly line with perfect accuracy, so fixing that first will help a lot. For the guideline, yes, swap the pencil. A water soluble marker is the cheap and easy option, and it behaves well on most cotton or linen. Trace or draw your letters, check them in the hoop before you stitch, and wipe with a damp cloth when done. Transfer pens are handy if you like to draw on paper first, since you can trace your lettering over and over til it looks right, then iron it through. Whichever you use, draw the letters as single lines rather than outlining shapes, because thin single lines are much easier to follow with a stitch. The thread twist is a real culprit too. Every so often, let the needle dangle from the fabric so the thread can unwind itself, maybe every five or six stitches on a curvy section. Also keep your strands flat as they lie against the fabric, untwisted the way they came off the skein, and don't pull too tight. Tight tension plus twist is what makes a line go ropey and uneven.

On stem stitch vs backstitch, try stem stitch and I suspect you'll never go back for lettering. It makes a slightly ropey, continuous line that hides small inconsistencies, so curves look smoother even when your stitches aren't perfectly even. It travels left to right with the needle coming up on the same side of the line each time, and on curves you keep the working thread on the outside of the curve. Split stitch is the other one worth trying, it looks very similar and some people find it easier to keep even.

One last obvious one since you asked for those: stitch text with the fabric drum tight in the hoop and take your stitches slowly, one at a time, checking that each one touches the line. Speed is where letters fall apart. Once your hand learns the rhythm on a practice scrap, the quote piece will come togehter fine.

I'd push back on the idea that stem stitch hides small inconsistencies. In my experiance it does the opposite on small letters. The ropey texture that looks great on a big flowing quote just turns lumpy when the letters are an inch tall, and any tension wobble shows up as a bulge right on the curve. I stitched a name on a pillow once with stem stitch and ripped the whole thing out, redid it in backstitch with short stitches and it looked twice as clean. Maybe it works better at larger sizes, but for fine text I'd practice both on a scrap before committing either way.

I think the fabric grain plays a huge role too. I've found that if your fabric is cut diagonally across the grain, even with super short stitches, the tension just ends up fighting the weave and things get really wonky. It's always best to orient your fabric so the direction of the yarn runs parallel to the line you're stitching, even if it feels awkward at first. It makes the line feel so much more stable. Also, I usually make sure I'm bringing the needle up exactly where the pencil is rather than just at the end of the line.

For me the whole game changed when I stopped drawing letters freehand on fabric and started tracing them. I taped my printed quote to a sunny window, laid the fabric over it, and traced with a fine water soluble pen. Getting a clean line to follow was honestly half the battle for my lettering too. I did a wedding date on a pillowcase that way and it came out even enough that I stopped being scared of text. Also I use a shorter length of thread for letters than I do for fills, like under a forearm's worth, because short thread seems to twist way less on all those little direction changes.

I've found that the tension often changes if you just pull the thread a lot. When I'm doing text, I try to pull the thread loose after every few stitches instead of making one big pull at the end of the line. This keeps the fabric from pulling tight in one spot and helps the line stay consistent across the whole word, which is especially important when the letters get close together. I also like to use a little clip on the hoop near the edge to anchor the cloth so it doesn't shift while I'm working a tricky curve. It feels like a small thing, but it makes a big difference in how steady the stitching stays.