Assuming you can break 60 at all, of course.
I think that I could go through seven laps at about 80 a lap, and then start throwing in ~59s alternating with 200-meter jogs in two minutes to carry me to the finish.
This would yield...
9:20 at 2.8K
10:19.9 at 3.2K
12:20 at 3.4K
13:19.9 at 3.8K
15:20 at 4K
16:19.9 at 4.4K
18:20 at 4.6K
19:19.9 at the finish
Wow. Put that way, that's not looking very good. But fastest 55 ever is only 55, so I don't even know if the above would be manageable. I probably couldn't even break 20:00.