Ok, I should have looked at the pictures first...

You are on a flat bar bike, but you do already have the bar ends and gloves. I would check the seat angle first and see if it is tipped slightly forward. Next, I would try wrapping the bar ends with padded bar tape to make them softer to hold. I can't see what kind of grips you have, but they make "ergo grips" that have a large rounded area to rest your palm on. They come in mens and womens models that are different sizes depending on how big your hands are.

My wife added ergo grips to hers and wrapped bar tape on her bar ends and it completely fixed the problem for her. Then a year later, she switched to a regular road bike (Trek 5000 WSD...women's specific geometry) and now can't imagine how she ever rode so far on a flat bar bike.