OK, here is a revised version. I made it only one character going down instead of two. Can you guys verify what it says, I have: Endure, Respect, Thanks or Gratitude, and Discipline. Thanks.
Yes, I think this is better than your original proposal. Using single characters has the risk of misinterpretation, as many single characters have multiple, diverse shades of meaning, but as long as the meaning you intend is covered by a character, and the character doesn't also have any negative or inappropriate meanings, I think it is fine.
When it comes to art, which is what a tattoo is, after all, I feel that single characters are better than two-character words, as they are more abstract, and therefore convey ideas and concepts well. In fact, it is not uncommon to see art created in Japan that uses only single characters by themselves.
One additional thing you could do is add a tiny image or symbol of your own choosing between each of the characters, to make clear that they are separate from each other and not part of a longer multi-character word. And spacing the characters further apart from each other than normal vertically-written Japanese text will be helpful, too.
As for the specific characters to use, for the first one, I slightly prefer 耐 (part of your original two-character word) to 堪, but either is OK. For the last one, I prefer 修 to 躾. I assume that your intent with the word 'discipline' is along the lines of 'self-discipline' rather than being disciplined by others. If so, I think that is better conveyed by 修, which suggests personal discipline, including the use of personal discipline to bring about cultivation, self-improvement, and mastering of skills. The middle two characters are fine, I think.
Maybe it would be good to change the order, putting the middle two first and 'endure' last. That way, you start by giving thanks and showing respect for others in your life, and finish by showing your own determination to excel. That's entirely up to you, of course.