I don't know if a digital pedal is on your menu. The Source Audio "Dirty Trinity" (LA Lady, Aftershock, Kingmaker) are essentially the same pedal, but with different presets pre-loaded. For example, the LA Lady can easily configured to become an Aftershock by loading the six Aftershock presets via the Neuro app. I only mention this because you might find a deal on any one of those three pedals, and they're all three essentially the same. They have dry mix and lots of ways to preserve low-end. Demo vids are out there, but it's hard to find those that match one's particular tastes & needs. Still you can see from the demos how the pedal does have a good analog character. I can assure you that it is a very versatile pedal and has very low latency (less than 1 ms)
Here's the available drive-types list. Some of them are asymmetrical, but I don't know which ones get into sawtooth territory.
0 Tube Drive - Marshall amp-style overdrive
1 Smooth Tube - Mesa boogie pre amp distortion
2 Power Stage - Fulltone Distortion Pro
3 Crunch Tube - Our own distortion, not based on any particular sound. It’s a more aggressive tube distortion.
4 TS9000 - Ibanez Tube Screamer
5 Big Pi - EHX Big Muff Pi
6 El Raton - ProCo Rat
7 Fuzz Façade - Dallas Arbiter Fuzz Face
8 Bender - Tone Bender mk II
9 Metal - EHX Metal Muff
10 Octave Fuzz - Octavia
11 Gated Fuzz - inspired by the Woolly Mammoth, but not very close at all. (rsmith601's words, not mine)
12 Bass Tube Drive
13 Bass Smooth Tube
14 Bass Power Stage
15 Bass Crunch Tube
16 Bass TS9000
17 Bass Big Pi
18 Bass El Raton
19 Bass Fuzz Façade
20 Bass Bender
21 Bass Metal
22 Bass Octave Fuzz
23 Bass Gated Fuzz
24 Gated Fuzz II - original
25 Gated Fuzz III - original
26 TS 9001 - Ibanez TS 808?
27 Maestro FZ-1A - Maestro FZ-1A
28 Bigger Pi - Skreddy Mayonnaise
29 Foldover - original
30 OhSeeDee - Fulltone OCD
31 Fuzz Face II
32 DS-1 - Boss DS-1
33 Rat II
34 Bender II
35 Metal II
36 Octave II
37 Smoked Glass C4L - Darkglass B3K
38 38 Special - original
39 Smooth Tube II
40 Power Stage II
41 Crunch Tube II
42 Grated Bass - original
43 Clean
44 Smoked Glass D5M – Darkglass B3K
45 The Klone - Klon Centaur
46 Pepperface Fuzz - Analogman Peppermint Fuzz
47 Vari-Screamer - Nobels ODR-1 Natural Drive
48 Foldover II - Original
49 Germanium Muffin - Germanium EHX Big Muff