How can one atone for sins, including deliberate ones, and the feeling of distress and distance from Allah, with a desire for sincere repentance in Ramadan?

There is no great sin that Allah Almighty does not forgive if the servant repents with sincere repentance. The door of repentance is open before the death rattle, for Allah Almighty says: "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.'" And sincere repentance erases previous sins, for "The one who repents from sin is like one who has no sin."