I opened a Roth in 2017 and closed it in 2018, so I'm subject to the 10% penalty. If I open a new Roth (same $) before 4/15/19, can I avoid the penalty?

Unfortunately, you will not be able to avoid the penalty.  

You can roll over the distribution to another Roth IRA provided the amount is rolled over within 60 days from when you received the distribution, and the Roth IRAs were not involved in a rollover during the 12 months preceding the date of the distribution. 

Based on your scenario, you would be outside the 60-day window.