Read your variety descriptions...some parsnips will take all season to reach maturity by your first frost date. Some varieties will mature in 90-100 days...with a variety with a shorter maturation date, just count backwards from your average frost date and plant a couple of weeks before the date you counted back to. Parsnips will keep really well after the frosts start, and remember, their growth has stopped once they get hit with a freeze, so getting too big and "gnarly" as you say shouldn't be an issue. A good freeze is your friend with parsnips, it will make them very sweet, not tough!