How do I keep my carved lines from getting shallow halfway through a project?

Almost certainly a mix of two things: the surface of the leather is drying faster than it looks like it is, and your blade edge is going off between the start and halfway point. Both sneak up on you because everything still 'looks' fine. The color test everyone teaches tells you when the leather is cased, but it doesn't tell you when the very top layer has dried enought to stop cutting cleanly. On a big design like a figure with lots of linework, the first section can be perfect and the far half can be past the sweet spot even though it's still darker than raw leather. Try this: touch the back of your hand or cheek to the surface. If it feels cool, you're still good. If it feels neutral or warm, the cut will be shallow and grabby. Also mist the whole panel lightly from a spray bottle partway through instead of recasing overnight. A light fog and five minutes of wait gets you back in business without the whole piece going soft again.

The other culprit is the edge. Veg tan is rough on blades, and a swivel knife that starts the session cutting like a dream can be dragging within twenty minutes. Dragging blades also explains your ragged cuts under the magnifier. Pull the blade out and look at it under strong light, or gently draw a fingertip off the side of the edge. If it catches or has a burr, it needs a few licks on a strop with compound. Honestly, strop every ten or fifteen minutes of carving and you'll be amazed at the difference. Keep a scrap piece handy and test-cut a line on it whenever the cuts start feeling off.

One more thing since you're a few months in: hand fatigue is real. Your pressure at line forty is nowhere near line five, you just don't notice it happening. Cut in shorter sessions, re-check depth on scrap, and cover the work with plastic wrap while you take a break so it doesn't dry out on you.

The ragged edges might not all be sharpness. Mine stayed fuzzy no matter how much I stropped until I realized my barrel tension was cranked too tight, so the blade wasn't rotating with my turns and was sort of scooping sideways through the leather. Loosened it up so the barrel spins free and the cuts came out clean almost right away.

Worth checking since you're a few months in, easy to overtighten without knowing. Also the gunslinger design sounds cool, post the finished piece when you're done with it.

That barrel tension thing is so true. I fought fuzzy cuts on a belt panel for weeks before someone told me the same thing, and once I backed the nut off a quarter turn it was night and day. Turns out I'd overtightened it trying to stop the blade from wobbling, which was exactly the wrong fix. Now I spin the barrel with a fingertip before every session, if it doesn't turn freely with a little flick I loosen it before I even start cutting. Also works as a check after cleaning, gunk in there can make it stiff again without you noticing.