Yep, by far the fastest and easiest way to do the inside is to cut off the bottom using very sharp cutting tool and do the inside. Then reorient the bottom to match the grain and glue it back on ... Then finisdh turning the outside and finish it a well. That way you stand a very good chance of hiding the cut you made when removing the bottom.
One hint though ... Be sure and NOT get any finish on the cut edges as that tends to make for a dark line when cluing it back together. Just take your time and be careful.
BTW, very nice hollow form and the finish is also very well applied. What are the dimensions of the piece?