Since SpaceX has already built the "first batch" of satellites (delivered to launch site as of a few days ago), one has to imagine they've largely solved the manufacturing problem and reduced the cost from 250k per antenna.
Phased array is definitely the way to go if you can get cost down. No moving parts means fewer hardware/mechanical failures and less noise
Both of these are very expensive in low-volume.
Speaking of which, there's a neat project that sneaks into a particular Intel chipset and extracts the CSI (Channel State Information) from the wifi hardware so you can actually do things like estimate which frequencies are being attenuated [1]. It's out of date, but still shows the kind of live, complex, signal analysis that is possible with commodity-priced hardware.
In short, I think it is certain that a base station can be built for <$1000, and likely that it can be built for <$150, although without knowing the precise specifications, it's hard to say. We did a case study on this in my antennas course in grad school 3-4 years ago, and our ending numbers on our prototype designs (not fully built and tested, of course, but simulated and spec'ed out with real-world pricing) were around $150. I am certain that our design as it was would not work, but something similar to it likely would. ;)
[0] https://en.wikipedia.org/wiki/Beamforming [1] https://dhalperi.github.io/linux-80211n-csitool/
(This may something you already had in mind, summarized as "high-end FPGAs;" I just wanted to add some interesting color some folks might not be aware of.)
At the very least SpaceX would test the devices to see what effects the higher radiation would have. However it's not unreasonable to just have the software detect and reset itself, if a high energy event is detected. There are going to be a lot of these satellites and a lot of redundancy in coverage, so if one is down for a few minutes it's not that big of a deal.
http://blog.zorinaq.com/asic-development-costs-are-lower-tha...
I don't think you need to move the antenna, but you need a wide footprint and probably overlapping coverage between satellites.
How does Iridium work? I'd think this has already been done(quite a while back even).
Iridium uses an omnidirectional antenna which is fine if all you want is 1200bps. But if you want 5Mbps, you have to point the antenna. So Iridium is not applicable here.
The orbital period for a satellite at 550 km is ~01h 36m. That means any given satellite is going to be visible for a very short period of time, which means hand-offs will have to be extremely frequent.
The fundamental problem is this:
https://en.wikipedia.org/wiki/Two_Generals%27_Problem
Don't know how cellular handles this.
One is simple to engineer, but resources are limited and expensive. The other is extremely complicated to engineer, but resources are cheaper and more available.
In this case GEO systems are simple: satellite is stationary (ignoring slight drift which causes microsecond changes in latency), beams are stationary, antennas on people's roofs have no moving parts. However, the GEO satellite is extremely expensive, the spectrum it is using is expensive, and the GEO orbital slot is expensive. Also, it's so far away that it's high latency making online gaming nonviable.
LEO systems are extremely complex by comparison: satellites are moving, thus the beams are moving, antennas are moving (motor driven, unless using electronic phased array which are currently super expensive). With everything moving you have to do constant beam hand offs, doppler correction, etc. But, the satellites are much cheaper and the latency is much smaller.
Kudos to whomever can pull it off - there are several contenders other than SpaceX like OneWeb.