Rather than quote everyone, I'll just agree with all of you.
Tucker, how long have you had the car? Did you just get it and has it been this way since you got it or was it better in the past?
This really isn't a HARD problem to solve. You CAN get the car working correctly on a 6v system but it is tedious and frustrating to work through all the possible causes of your very common hard start problem. Checking grounds, cable size and battery are all great recommendations.
I've had this happen more than once. The last time it was the battery. Very easy to have the parts store check it out. If it is bad battery, replace it with an Optima; you'll never look back.
Not familiar with the '33 but on my car, after checking all the existing grounds, I found that whoever had refurbished the car 20 years ago had neglected to install one of the most important grounds, the one to the engine block. There should be a ground directly from the battery to the engine, or perhaps from the battery to the firewall and then another from the firewall to the engine.
COULD be the starter. Other folks have reported that. I removed my starter and found a lot of paint on the mounting surface. It should be bare metal. I scraped the paint off and polished both surfaces with a scotch-bright, big improvement. Could also be the starter itself.
Probably not the generator since the car runs with the battery disconnected.
Could be the voltage regulator. You need to check the battery voltage when the car is off and then check the voltage when the car is running at higher RPM, 1500-2000. You should see a slightly higher voltage indicating that the generator is charging the battery. You probably won't see the generator charging the battery at normal idle speed. You'll need a precise voltmeter to detect the slightly higher voltage while charging. My 0-25 V analogue voltage meter is worthless for this test, you can't see the difference. Many folks say a digital voltage meter doesn't work well on these cars but mine does.
I bought a very high quality Fluke digital multimeter to check things out and it worked great for me. I won't guarantee your results though. I'm a tool junkie, not flathead electrical expert.