By now, you've spent a bit of time around spiders, have thought about what it is that scares you about them, you've learned more about spiders, and you have written it all down. You have done a great job! Whici is why you are now ready for even more.
Having now noted what is upsetting to you, you can look more closely at the spiders in the exhibits at the museum or in the zoo.
Pay close attention to those aspects of the spider that you have found are most disturbing to you. This approach will make you uncomfortable, but it will also help you become better acquainted with yourself.
Whilst calming yourself using relaxation techniques, try moving your hand close to the glass of the display. Some establishments may not allow visitors to do this, so explain your situation to the attendant beforehand and they will likely understand or even help you. You do not need to touch the glass of the display - simply reaching out towards it is taking a level of control over your actions that you did not have before!
This can be done as slowly and over as much time as you need. Just make sure that in the end you do it, rather than give up. Before you try the approach, take some time to set specific goals. These can be things like "This time, I am going to get halfway before I let myself pull my hand back". The ultimate goal is to have your fingers almost touching the display.
Although it will be challenging and perhaps even upsetting at first, gradually you will find yourself having an easier time approaching the glass. Make sure you repeat this step at least twice or thrice per week, over several weeks.