Thanks for playing!
Both of your suggestions are good but I did consider them.
The reason why it's not there the whole time is because it is directly linked to how much time you have to complete the level. The more you restart, the longer time you have. A restart button does appear when the timer runs out.
Also, the timer starts straight away to force players to think quickly, rather than plan out their route and finish on their first try.
And nice, you made it :D