That juddering you're seeing at low PWM settings is a very common issue when using geared DC motors, especally if those are worm gear types. It's usually not just the duty cycle, but the interplay between the low torque output of the motor at low speed and the static friction of the mechanism itself. Worm gears, specifically, often have a high backlash or mechanical resistance, meaning they need a certain amount of rotational force just to break free and start turning. If your duty cycle is so low that the motor's low-speed torque output is weaker than that static friction, it will stall or chatter before it can actually move the desk smoothly.
What you are likely experiencing is a mechanical torque threshold. Even if you are providing a steady 5% duty cycle, if the motor can't generate enough current to overcome the physical resistance of the gears and the load, it will fight against itself, causing the judder. Your current sensor spiking confirms it's trying to draw more power than it's actually being supplied in that low PWM range. You mentioned you have a 20A threshold, which is plenty of headroom, but the issue is likely insufficient sustained torque at that frequency.
Since you want smooth creeping, one simple check is to see if there is any way to slightly increase the average voltage or current delivery at the lowest possible PWM settings, even if the motor is just barely moving. If the motor is under a very light load, sometimes a slight bump in power helps it overcome the initial sticking. If that doesn't work, you might want to look at the gear reduction itself. If you've used a very high gear ratio, the torque at the output will be massive, but the motor has to work harder just to turn the gearbox itself when moving slow.
Another option, though more complex, woud be to switch from pure PWM speed control to a method that controls the voltage directly while also monitoring current, but for a home setup, dialing in that mechanical resistance is usually the first and easiest step. Try reducing the mechanical load by ensuring the system is perfectly seated and nothing is binding before you push the duty cycle down.