With a 55 in the quarter, you're gonna need to run about a 4:35 in the 16:00 to meet your Goal.
However, you run a 24 200m. With that, I'm HIGHLY confident that you could run a 53 400m at least.
With a 53 second 400m, you'll need to get your 1600m down to about a 4:45.
If you really push yourself & get your 400m time to a 52, then you'll need about a 4:50 to meet your goal.
Here's a quick little chart for you to see what you need to run in the 400m/1600m to run a 2 FLAT
400m / 1600m:
50s / 5:00 - 5:05
51s / 4:54 - 4:59
52s / 4:48 - 4:53
53s / 4:42 - 4:47
54s / 4:36 - 4:41
55s / 4:30 - 4:35
So if you stay at your current speed (55s 400m), then you're gonna need to run about a 4:35 1600m to meet your Goal.
However, judging by your 200m time, I KNOW you can get to a 53s 400m (I ran a 24/53 with little endurance). Once you get there, you should try getting you 1600m down to around a 4:45 and you have a pretty likely chance of reaching 2 FLAT.
Even if you don't get your 400m to a 55s, then you could easily get it to a 54s. In which case, you'll need to get your 1600m to about a 4:40. Not too far off from your current PR of 4:50.
So, I'd suggest you get your 1600m down about 10-15s and/or your 400m down 1-2s.
GOOD LUCK!