Based on your description, it sounds like even though you will ride it in the 'wet', you won't necessarily go through 'wet mud'. A lot of 'wet' tires (Schwalbe G-One Ultrabite, Vittoria Terreno Wet, Panaracer Gravelking EXT, Continental Cross King) are designed to excel in wet, muddy conditions, and have a tread pattern that sheds mud quickly. This comes at a significant cost of rolling resistance.
Therefore, I wonder if a more regular gravel tire (with a faster tread) would be a better fit.
Bicycle Rolling Resistance and
this German magazine test are a great place to start.
If I were you. I'd consider:
- Continental Terra Speed 700x40c (which have a tendency to run narrower anyway)
- Panaracer Gravelking SK+ 700x38c
- Pirelli Cinturato Gravel H tyre
Good luck!