Connection is your first priority. Yes poor connection to the starter or to the ground will be worse than a bad battery.
You say the battery is only a year old. By that you mean you bought it a year ago? How long was that battery sitting on the shelf. Remember, 6 volt batteries do not sell on a regular basis. When whom ever put the acid to that battery is when that battery started growing old. If you have the receipt. Put a charge on the battery and take it to the place that sold you the battery. Have them do a load test. I have a suspicion it will fail quite quickly. You will get a new battery, the worst scenario they will try to discount one year of value (forgotten the term for this practice).
The common problem with a generator is going to be the regulator. The generator seldom goes bad except for bearings or brushes. The windings can go bad if the regulator is allowed to cook the generator. Yet the amp draw to do that will do two things. 1) a battery charged generator will keep the motor turning after you turn off the ignition. 2) Melt the wiring from the battery to the regulator (you would notice the melting as soon as you shut off the switch, it is that quick). Also if the regulator is mounted like the 420 crawlers in the dash, melt the wires from the regulator to the generator. I did have a problem with my crawler where the water probe wire rested onto the regulator and shorted the generator that way, so keep in mind, any metal contact, no matter how small will also drain a battery.
With the battery cables removed from the battery. Attach a battery charger to the cables. A sensing draw from the regulator would be less than a quarter amp and would barely twitch the needle. If the regulator is shorting out, the needle on the charger will easily snap over to 20 amps. A bad ignition switch will be about a 2 amp draw and usually keeps the points hot. There are not alot of items on a JD tractor that will pull much power.