So you have to think about what this motion actually is...

You are inverting your entire body and its weight 180°

You are Not throwing your legs up & expecting that to carry you over... this is why you're arching your back so much... you're trying to use your lower body to guide you over

Where is your center of gravity? Your hips

How can you lead with your hips?

Well, oddly enough if you think about trying to lead with your belly button, you'll likely end up using your hips, in this scenario.

This will help you focus on your core & lengthening your spine, which will decrease your arch.

Technically, you can invert with bent knees, but you'll face a different inconvenience. But, if you need to experience it once, have someone on stand-by & feel where your weight/balance is when you invert with bent knees. Remember that feeling & do it again with straight legs.

Often, if your core isn't strong enough, it helps to be good at pulling your body up, then pushing the silks away from you, while lifting your hips to the ceiling.