@jsbeckton, I suspect you're leaving a gallon or two of wine behind.
Last year was my first time using fresh grapes in 20 years, so I re-learned a few things. The first run wines I pressed light to medium, and made a second run from the pomace, adding 15 gallons of water to the pomace from 540 lbs grapes.
I pressed 15+ gallons of 2nd wine from the pomace, which went into a barrel. Then I pressed hard, producing another 7 or 8 gallons. I kept this segregated. It was more strongly flavored and definitely harsher than the lightly pressed 2nd run.
By last spring, the hard press had changed dramatically, softened and lost the harshness. I used it to top up other containers (including the 1st runs), and bottled a carboy in August. Side-by-side, the light press 2nd run (spent 10 months in a barrel with 6 oz Hungarian oak) and the hard press 2nd run (no oak) are completely different wines. I'm surprisingly pleased with both.
My recommendation: press your wine are hard as you feel comfortable with. Then use a different bucket and hard press the remainder. Keep the hard press separate and evaluate it over the winter and spring.
If it's not good? You've wasted a bit of time, but have increased your knowledge, IMO a good trade. If it's good? You have a few more bottles. Also, if you like the hard press, experiment with blending it with the light press. The hard press wine's heavier body may make an improvement overall.