I noticed a couple issues with my '87 FC NA after a recent track day and I'm hoping to solicit advice.

My car is making stock power, and has had all emissions/cold start equipment removed along with the air pump. It has electric 5th/6th port actuation.

1. Transmission Synchro Issue

There is a grinding noise when moving the transmission into gear during the downshift from 4th to 3rd. It happens probably 80% of the time. I'm assuming it's a bad synchro ring, but I don't have a lot of experience with transmissions. If it is a bad ring, how difficult would it be to replace?

2. Warm Start Issue

The car starts fine when cold, (keeping in mind that with the cold start system removed you must hold the throttle for a minute or two before it will idle), but when the car is shut off when warm, it refuses to start back up normally. If we bump start it, it starts right up. I've also been able to get it to start by giving it a little bit of gas when cranking it. Other than this it seems to run normal. Is this just a characteristic of the car after removing all of the cold start system and related components (I have not run the car much since doing that), or is there something not working correctly?