I can show you how to update the php.ini file. It is a simple and relatively common thing to need to be updated. I will usually update the php.ini in almost all sites I develop.
I can also update the persist code so you don't need to. The persist code assumes the default value for that setting and for some reason yours isn't configured with the default. I can pretty easily make that update and send you the new persist file.
The issue is that the persist saves the entire $_REQUEST value as a cookie, and with the configuration you have set up the cookies are included in the $REQUEST and cause the effect of exponential growth of the cookie as more persist values are set. They include the current form and all others in each.
If you want me to send you an updated persist file or help you update your php.ini file in a screen share just let me know and I can set up a call.