Hi Meg - you can't 'vary' a form LL restriction as it's a standard form so your idea/suggestion can't work
If you want it to remain on the register then you'll need to get a conveyancer to provide the certificate as per the wording to submit along with your remortgage.
If you want it removed (form RX3) you also need a conveyancer's certificate
As an aside some conveyancers apply for the form LL restriction when acting for a buyer as 'part of their service' offered at the time. I suspect that's what happened to you as you mention that you have 'found' it on the register when you came to remortgage
The form LL is one of three things we recommend/offer to help owners minimalise the risk of property fraud. The other two, and which are not restrictive re future dealings with the property, are keeping your contact address up to date and our free Property Alert service -
Property Alert - GOV.UK
The third, and form LL option, is primarily aimed at 'absent' home-owners. For example a landlord renting out their property or someone who owns more than one property. No reason at all that property owners can't opt for the form LL option but it will add that extra restrictive hurdle as you have now found out