How do the spark plugs look? Are they black and covered with soot?

 

It takes a lot of Oomph to start a big twin cold. Look to the battery connections, the condition of the battery and how corroded is the connection between the ground strap and the frame or engine?

Mine had symptoms much the same and correcting those faults cured it. And it now dislikes the choke when cold.

 

Make sure your air filter is clean also. It's easy to neglect on a bike.

Not sure of the age/history of your Hawk. You might want to check the vacuum hose that opens the petcock valve.

 

Carb sync?

 

replace your RR. mine was doing that last year. I would have to hit the button and then slowly pull the choke out till it caught. it was turning over, but too slowly to catch. it was the RR. it had lost charge overnight. and same as you, once it was going I'd ride to work and when I went home, it fired up no prob. until it didn't. I stopped at a gas station on my way home one night, and when I went to start it, all my electrics were dead. I had to coast it down a sidewalk for a mile to get it home. new finned RR later, good as new, no probs since. sometimes those RR's will die very slowly. mine was doing it for the majority of the season before it finally quit. so several months at least.