Here is a strongly invertible diagram of 10_49. The symmetry axis is almost horizontal.

[![enter image description here][1]][1]


This was created by loading the 'standard' diagram of 10_49 to [KLO][2] and then using KLO's simplifying method together with some work by hand. (KLO's simplifying method seems to prefer symmetric diagrams this is why I would expect the method to work in most cases.)

We have used similar methods for example
[here][3] to create strongly invertible surgery diagrams. I would expect that the same works for the other 7 knots from your list. If you need help with that let me know.


  [1]: https://i.sstatic.net/7ZnS4.gif
  [2]: https://community.middlebury.edu/~mathanimations/klo/
  [3]: https://arxiv.org/pdf/2203.12013.pdf