A project such as this is usually way over the head of someone who does not do this work daily. Hence the reason I suggested earlier to hire a pro. They have to eat too you know! The real problem here is safety. Not only yours but others. I lived with the NEC and inspectors for over forty years. I also had a UL508 certification for building industrial control equipment.
Please, if you won't believe me, believe uncle harry, when the code says you shall, it means you "WILL". No arguments, no exceptions, no nothing.
Also if you have not checked into it yet, depending on what starter you are dealing with, the parts can be hard to find and damned expensive when you do. Translation, you can probably buy a used starter for way less then two replacement coils. Go on fleabay and look up reversing starters. I have found units there so cheap compared to new it is crazy. I have purchased units good for 5hp for as little as $40.00. Only thing left then is to find the correct heaters for the overload block. All manufacturers have changed to electronic adjustable overloads making finding separate eutectic heaters a harder and more expensive venture. Keep this in mind when choosing a starter. Also, believe it or not, electrical components wear out. Just like most other things so maybe a newer starter even has more merit.
Even after all these years I still do not feel relaxed around 480v equipment like I do at the lower voltages. Just be safe, 480v will kill you in less than a heartbeat.