Restricted Category to Normal Category

Actually, what you're looking to do is exchange the Special Airworthiness Certificate in the Restricted Category for a Standard Airworthiness in the Normal/Utility Category.  See 14 CFR 21.175.  In any event, what you'd need to do is return the aircraft to a configuration compliant with its type certificate.  That would mean having an A&P remove any equipment not part of the TC (or any appropriate STC's) and/or undo any modifications otherwise not compliant with the pre-Restricted configuration, and certify completion of all the items for a 100-hour inspection of that aircraft*.  Then you get an IA to certify any major alterations involved, and finally have the FSDO or a Designated Airworthiness Representative (DAR) examine the aircraft and issue a new Airworthiness Certificate in the Standard Category.  This is covered in FAA Orders 8900.1 and 8130.2 (Chapter 3).  Contact your local FSDO for details.

*"...inspected per the performance rules for 100-hour inspections in § 43.15, meaning use of a checklist that includes at least the scope and detail of appendix D to part 43..."