Do you count Salt Cure as a damage over time move? Contains a direct damage component (40 power) as well as damage over time. Recommends Garganacl, if you do.
Views Leech Seed as a good move, particularly totems. Could go Breloom with Spore + Leech Seed. (Requires level 40 on Shroomish, though.) May be able to snag Leech Seed + Ingrain with a Leftovers (Cacturne, Sunflora, Lilligant) for tons of passive healing, alternatively.
Cannot ask about damage over time without mentioning Toxic and Toxic Spikes. Points to Toxapex as an excellent option for both. Brings solid durability and longevity.
Obtains a Rocky Helmet from defeating trainers in South Province Area 4. Apparently becomes available in Mesagoza at 4 badges too. Cannot pair it with Rough Skin, unfortunately. (Appears on the Carvanha line and Druddigon line naturally, who are not in Scarlet/Violet. Grabs it on the Gible line as a hidden ability.)
A more off-the-wall strategy: Scovillian's Spicy Extract (+2 Attack / -2 Defense for the enemy Pokemon) + another Pokemon's Confuse Ray. Ought to hit itself hard. Requires foreknowledge of the enemy's moves, however. Risks getting demolished otherwise. Relies on randomness for the Pokemon to hit itself too.
Do not forget things like status moves (such as Burn) to help keep your Pokemon in good shape. Might also be well-served by offense lowering moves like Charm, Feather Dance, and Eerie Impulse. Allows another Pokemon to pop in and set up Amnesia/Iron Defense for the rest of the battle. Learns the Charm + Eerie Impulse pair on Jolteon, Raichu, Pachirisu, and Pawmot.
A few other options:
- Sandstorm (through Hippowdon's Sand Stream, perhaps).
- Binding Band / Grip Claw. Raises damage and extends the duration of binding moves, respectively. (See: Bind, Clamp, Fire Spin, Infestation, Sand Tomb, Whirlpool, and Wrap)
- Stealth Rock, Toxic Spikes, and Spikes on Forretress.
- Rest. Keeps your Pokemon healthy and status-free.
- Phasing moves with entry hazards. Spots Spidops with Circle Throw, Spikes, and Toxic Spikes.