Just curious so can you explain what was the issue you faced using the Mailgun free plan? I have used their free plan in the past and never faced issues with reliable delivery and the emails were never marked as spam.
This was about 8 months ago -- had never used Mailgun before. I was seeing nearly 30% "dropped" messages (rejected by receiver due to sender reputation). They did move me to another IP which worked much better, but the first impression on users was already made. I didn't push it too much because after all I wasn't paying for it so didn't really have much standing to complain.
Did you warm up your mailing list? I've seen an issue before, but it was down to our domain being new for email and us not knowing to gradually ramp up the emails instead of sending many from the get go.