Workflow 1: feed a sawtooth oscillator through filters controllable with knobs. Eventually I realized that it will always sound mechanical, no matter how many filters you stack. That led to
Workflow 2: feed a sawtooth oscillator through a convolution reverb that uses a custom impulse response. For impulse responses, use random sounds downloaded from the internet (like wood strikes), or mixtures of existing instrument sounds. But that felt limiting, so I moved on to
Workflow 3: generate an impulse response wav file with Python, and use that in a convolution reverb to filter the sawtooth. This gave me some more interesting and configurable echoes, but then why start with an oscillator at all? So
Workflow 4: write code to generate the sound on the fly, as a sequence of samples. This way I can mimic some nice properties of physical sounds, like "the nth harmonic has initial amplitude 1/n and decay time 1/n". Also I can get inharmonicity, smearing of harmonics (like in PADsynth algorithm), and other nice things that are out of reach if you start with periodic oscillators.
If I could go back and give advice to my months-younger self, I'd tell me to skip oscillators and filters, and jump straight into generating the sound with code. You need to learn some math about how sound works, but then you'll be unstoppable. For example, here's a short formula I came up with a month ago for generating a pluck-like sound: https://jsfiddle.net/yd4nv5Ls/ It's much simpler than doing the same with prebuilt bricks.
The whole experience made me suspect that there's an alternative approach to building modular synths, based on physical facts about sound (as opposed to either starting with oscillators, or going all the way to digital modeling of strings and bows). It would be similar to physically based rendering in graphics: for example, it would enforce a physically correct relationship between how high a harmonic is and how long it rings, and maybe some other relationship about what happens to harmonics at the start of the sound, etc. But I'm not an expert and can't figure out fully how such a synth would work.