Honestly, I think you have a real chance at sub 18:00 right now.
You say that is 3k pace, but with rest that short relative to your work bouts, and with 8 intervals, I think that this is probably closer to your 5k pace than your 3k pace. My only hesitation is that 800s are just short enough for you to power through them at a faster pace than you would normally expect to be able to replicate. Cutting against that concern is the short rest, the high number of intervals that you ran and the fact that even though these were 800s, they were still nearly 3:00 intervals, which is a fairly long bout (and thus harder to "fake").
I would do follow up workouts of 6 x 1000 with 2:30 of active rest (jogging)and then 5 x 1200 with 3:00 of active rest, both run at 5:40/mile pace. If you can do those workouts in the next few weeks, I would encourage you to be aggressive in your next 5k and go out at 5:40 pace.
Were your intervals consistent across the workout? At what point in the workout did you reach the "I am not sure I can finish all 8 of these in the prescribed time" point of the workout that we all reach at some point?