Shining through you window is pretty much the only valid reason i would ask for them to move it. Infact they probably HAVE to move it.
If you go on about wildlife etc. you will just dilute your argument.
For what its worth i kinda agree with you about the wildlife. However, i have all the above in my garden and they don’t seem to give a shit about the lighting from all directions. Including some quite potent floods from a neighbouring commercial premises.
For clarity. I 100% agree with your efforts for encouraging wildlife. I am just not convinced your lighting issue is as bad for it as you suggest for the hogs moths and bats.
Edit2. You’ll get her with a statutory nuisance. From the Clean neighbourhoods and environment act 2005.
Not saying it would be easy or worth it but you have the law on your side.