The voltage you measure with that test is the battery voltage, not the charging capability of the alternator. Hence all you have shown is that your new battery has not completed its plate-formation process yet, and it won't achieve higher voltages until it has. The only thing you know about your alternator is that it is putting out enough charge to raise the voltage across your battery by 0.3 Volts. From memory, it is a 3 Amp alternator.
I would be very surprised if your engine has a voltage regulator for a tiny alternator like that. All it will do, is put its puny 3 Amps into the battery when it is running flat out, and proportionally less at other times. 3 Amps will not hurt a battery that size, even if it is fully charged already.
On another subject, those mesh screens in front of your headlights will be costing you about 25% of your light output. I don't understand why you used them. They won't protect anything against bumping into solid objects, and I doubt your ride on mower will encounter many small stones thrown up by vehicles at highway speeds.
