I didn't know outside special events you are allowed to cycle through the Queensway tunnel overnight, however wouldn't bother given it's length, & narrow lanes, not sure what the gradient is either, the bends in the tunnel are so it avoids building foundations, particularly at the Birkenhead end
On another note, buses are £2 for single fare, i think the £2 single fare is staying for the Liverpool City Region after the English national £2 single fare scheme ends in June.