Re: "AIUI the military signal has a faster chipping rate with longer PRN "
Civilian GPS really is 1023 chips/cycle so the PRN shift-and-feedback 10-bit register never has to go through zero, 'cos if it did it would stay on zero. Repeating every millisecond (nominally, subject to doppler and clock errors).
About the mil signal, the really long cycle time is for security only - makes it really hard to find unless you have pre-loaded tracking data somehow, from that encrypted almanac as you say. But that aspect doesn't add at all to accuracy: only a higher chipping rate can do that, which as you say is 10x the civvy version. But only 10x, so each chip is ~30m. You might get 30cm correlation data out of that.
The ionospheric correction - the naive algorithmic one (ramps up linearly from 0600 local to noon, ramps down from 1800 local to midnight, times cosine something I think) in civilian GPS standards docs anyway - is under 10m, ISTR it being 5m to 7m max usually. So the naive model is good for a system whose overall accuracy is 5-10m anyway. Interesting that of course the mil system needs better Iono corrections from the ephemerides (I guess) 'cos its native accuracy is higher.
But it can never be reliably that accurate. I had a GPS antenna on the windowsill of an office about 15m up. It saw half the sky OK. I generally got accurate positions, being of course the position of the antenna not my computer connected to it. But when it rained, a sloping roof across the road turned into a radio reflector and I could "see" much of the other half of the sky too. Great! you might think, but it saw the new sky with extra path length, since the new signals went across the street and back extra. So my positions were solved for about 10m away, in the middle of the road. Ain't nuthin' you can do to prevent that sort of situation short of rejecting some signals in the solver - but which ones? - whatever your chipping rate and correlation accuracy, it can still be fooled by reflections.