Fullview storm door

In 1995 I built my home and installed a Fullview storm door on the front, It has an interchangeable screen or glass insert. About every 3 or 4 years I need to work on the screen and I am beginning to think there has to be a better way. I dug out my invoice to determine the brand of door. I purchased at Payless Cashways which is no longer in business. On the 8 thumbscrew tabs that hold the screen or glass in place, it says EMCO but all the invoice says is FV-36WH Fullview white. There is a very weathered sticker on the hinge edge that says The Forever View EMCO. Now to my question....replacing the screen, I have a flat rubber piece that measures about .080" x .330" that does absolutely a terrible job of holding the screen in the channel, works good till someone pushes on screen then its all over. The channel measures about .120" deep x .340" wide and has a slight undercut on each side, the outside maybe .030", and inside maybe .062", I hope you can see in pictures. Was thinking about the 55-109 spline...Your thought.