Classic/Antique Car Repair: La Salle starting problem, earth connection, ground cable

Question
I have a 1927 La Salle restored which starts easily when cold but grinds over
very slowly when starting after running for a period. Sometimes I have to wait
for a while before it will start again, and often it then only fires when I take
my foot off the starter button.
The car is 6 volt and the starter has been restored including a rewind. Getting
very frustrating as otherwis ethe car is great. Any ideas. I think the earth
connection is good.

Answer
I will tend to disagree with you. 80% of the time I have seen this it has always been the ground connection. The other 20% was lack of heat shielding around the starter.

If all else is normal, which it should be if it starts fine cold, my money is on the ground cable. pull HARD on it everywhere and see what happens.

You have stated timing and all has been checked.