I think we may see the current 14-day period stay the same or increase before it decreases. If not, that would be one data point in favor of a ramp above the 2000/week range (but only one data point -- I think you have to look at the big picture).
Tesla registered 2655 VINs on March 23 (through 18540), 2041 more on March 30 (18541-20581), and another 4,793 on April 5 (through 25374).
If we see the next batch of VINs appear by about April 15 (16 days from March 30) that would be consistent with a solid 2000/week run rate (2655 VINs/9 days (April 6-15)*7 days/week=2065/week) -- any faster would be consistent with a run rate above 2K/week. But this is only one metric among many so I would caution against relying on it too much, especially since Tesla can decide to change how and when it assigns VINs to customers at any time and it already seems to vary quite a bit based on geography, etc. Also, there can be a lot of variability and looking over short time frames can be especially prone to error. As one example, if they shut down production for two days to increase speed of the lines they might not need the next VIN batch as quickly so tracking VIN use might suggest a slowdown when in fact production rate has increased significantly.
But having said all that if we were to see the next batch reported in a week or so (~April 15) that would be one data point in favor of Tesla continuing to meet or exceed 2K/week.
As far as 5K/week I seriously doubt Tesla is targeting that by end of April and would be thrilled to see them in that range in July.