I thought I'd give some tips after swapping out the front and rear badges on my Zed as it's a bit of a pain in the arse tbh.
I initially tried heat (gf waggling a hairdryer) and dental floss. Dental floss is not strong enough and will snap, fishing line is better but can also snap if pulled against the sharp edges of the badge. With any type of line, be very careful about pulling it out wide against the sharp edge of the recess as it can nick the paint where it's thin. The other problem is that the badges (at least the rear one) have plastic locating lugs which will stop you pulling the line more than a 3rd of the way across. What I suggest is making a fishing line garot (!) around 8" long that's 3-4 strands thick (I looped it through the metal clips of clothes pegs to make a handle). Use your fingernails to push the line into the gap around the side of the Nissan portion of the badge (tricky) and pull slowly sideways as the glue begins to go soft (1 person with the heat, another pulling is ideal). When it won't pull through any further and gets stuck on the lug, pull the line towards you and use it to lever the badge away slowly. Try and get your fingernails or a piece of card under the opposite end of the Nissan portion of the badge to prevent it digging into the paintwork as you lever it away. Once it's off, roll the remnants of the sticky pad away with your fingers. Tar/bug remover was good on the tricky bits here, but it was pretty easy to get off. Give it a good clean before you apply the new badge. The 370Z badge comes off very easy by just pulling straight through, there are no lugs.
Applying new badges can be quite tricky on the front as there are no locating lugs to get it perfectly level with the recess and you won't be able to remove it after. On reflection I'd probably stick some tape to the new badge either side so I could place it down without fingers blocking my view. I reckon if it was slightly off, you could heat it up again and reposition it slightly with some force.