Your arithmetic getting to 50 birds per plane about 7° apart seems reasonable. I would be surprised if 50 satellites could be put on a single launch, if for no other reason that I don't think they'd fit in the fairing. Regardless of how many go up on a single launch, I think we can safely assume it would be more than one, in which case the answer below is still relevant.
What you're talking about is known as phasing the orbit of a spacecraft within its orbital plane, and yes, it’s a common problem that arises when multiple spacecraft are deployed from a single launch vehicle. There are a variety of ways to solve this problem that depend on the capability of the satellite, the launch vehicle, the orbit, and the constellation concept of operations (most specifically how critical the spacing is and how much time you're willing to spend between launch and everything being in the final configuration).
The Orbital Mechanics of Phasing
Ideally, phasing only changes a satellite's relative true anomaly with respect to the other satellites in the same plane. (I say relative because the TA changes continuously during an orbit.) A very straightforward way to do this is to temporarily change the orbital period by changing the orbit's semi-major axis. For example, consider a satellite in a reference orbit with a 90-minute period: a satellite progresses through 360° of TA in one orbit. If the orbital period was changed to 60 minutes (implausible, but we’re illustrating a concept), after 60 minutes one satellite would have a 360° change in TA, but the reference satellite would have only gone through 60/90*360 = 240°. If the 60-minute satellite was then restored to the original 90-minute orbit, the two satellites would then be permanently 120° out of phase.
In practice, such an aggressive maneuver would require a prohibitive amount of propellant. So typically the semi-major axis is changed in less dramatic fashion, and the per-orbit drift in relative TA is allowed to integrate up over several orbits. This process can take an arbitrarily long amount of time.
Luckily, the ΔV required is small if you have some time. A 180° phasing in a 450 km orbit can be done for single-digit m/s of ΔV if you have 3-months to spare. (Exercise to the reader, or perhaps a good topic for another question.)
Many satellites don't have propulsion but still need to phase. For example, Planet's Dove cubsats do not have propulsion. As presented in this paper, they use drag to induce phasing. By controlling each's satellite's attitude they change its cross-sectional area and drag coefficient, which changes the relative drag. Drag reduces the semi-major axis of an orbit and thus it’s period. They're using the atmosphere like a low-thrust, always anti-velocity-pointing propulsion system.
All the Fuels
Obviously the more straightforward approach is to use an on-board propulsion system. In the Seattle announcement of its communications constellation, Elon Musk indicated their satellites would have propulsion. (Note: I don't have a time-stamp, perhaps if someone watches the video and finds it they can edit this answer.) Given this, the satellites will likely be deployed by the LV into a baseline insertion orbit and then each satellite will use on-board propulsion to maneuver to a phasing orbit, wait until its relative TA is appropriately phased, and then maneuver back into its operational orbit.
A few weeks to get the phasing right should be no big deal because the satellites are likely designed to last for years — a small fraction of their operational life. Also, satellites typically go through on-orbit checkout activities just after launch that probably don't depend on operationally representative relative phasing.
Obviously the rocket upper stage can initially deploy each satellite into a phasing orbit (i.e. an orbit slightly different than what's desired for nominal operations), but the second maneuver that puts the satellite back into the baseline orbit after phasing is complete would still need to be done by the satellite because the rocket's mission would be long over.
I'd consider deploying an entire plane of satellites into a slightly elliptical phasing orbit and have each satellite circularize itself when it had reached the right relative velocity (so one ASAP, and then each subsequent satellite at a fairly regular frequency thereafter). Or if you had the ability to do at least one restart I'd use two phasing orbits: one with a longer and the other with a shorter period than nominal. That way half the plane's satellites can drift one way and half the other. This would approximately halve the time required to fully deploy a plane.