In the games after I explore half the sector, I find at least one synchrotron when I need one, but the number of excess synchrotrons found varies. Some games, I found several extra, but others I find only one or two more.
As for pristine nanoforge, I did not find any in half of my games before exploring half of the sector, and I had to raid core worlds for it. In one of those unlucky games, I found one at the left side of the sector after I completely explored the right side. As for the other half where I got lucky, I found only one. In one game, one was from salvaging a station (with no skills in Salvaging; would not have found it if Salvaging had points). Another game, I had a lucky early haul from a tech mine, but did not find anymore pristine forges after that.
I find about a dozen or so corrupted nanoforges in each game.
For blueprints, after aggressive tech-mining and exploring about half of the sector, I find about half of all of the blueprints... which leaves the other half to be stolen from core worlds through mind-numbing Diablo 2-style magic-find runs. From the looks of the patch notes update, it seems like blueprint drops will be reliable enough to eliminate or greatly reduce the worst of item grinding tedium (that online games tend to encourage).
For item drops, pristine nanoforges seem too rare. Synchrotron seems okay.
I do not sell those items (aside from exploiting Commerce bug, which will be gone soon). I hoard them all in case I decide to plop down a bunch of alpha-governed colonies someday where I can put all of the spares to good use. (I have not done so yet.)
Re: motherships
They are rare enough that you do not always find them when you need to. (e.g., They are left of core, but you spend years sweeping right of core.) Also, I read that they can drop corrupted nanoforge instead of pristine nanoforge. So even if you find a mothership, it may not have what you want.