Could you make it so that recipes are unlocked at the same time as logistics research in the same tier? Or is it possible to add a setting that would allow for this?

There is a mos setting for that already. Set "Unlock mode" to "With belts"

Does “mos setting” refer to mod settings? I can't find the “Unlock mode” option. There may be a conflict with some mod.

It appears that when used in conjunction with Space Exploration, some settings are disabled.

Oh, you are correct. That is in line with how SE treated loaders when Loaders are installed. AAI Loaders, Mini-loaders (in 1.1) were all intended to be their own tech. When those mods were installed it would even pull the K2 lower tier, K2 loaders into the separate tech.