Open source library to calculate image from signals of a distributed set of radio dishes?
This is an interesting question!
I'll post a partial, preliminary answer and let's see where this takes us.
The NRAO block quote mentions two methods, interferometry and intensity mapping (like how a camera works). There may be hybrid options and other esoteric options, but lets look at these first.
See also this answer to Which techniques are used to convert radio signals received by antenna to images? and since there are so many good answers to Radio telescope targeting those might be worth a good read as well.
Interferometry
This is where all dishes point in the same general direction and you have:

...the exact location(s) on the globe, knowing their exact time-stamp(s) of observation...

and those time stamps must be made to nanosecond relative accuracy; you use the phase information of the radio waves. You either hook them up with coax or fiber optic cable in real time, or write at up to gigabit/second speeds to hard drives and then cart them all to one location and run a very very big and special computer called a correlator to analyze the data.
Intensity mapping
This is just making an intensity map by sampling many spots in the sky and building up a histogram; basically exactly like how a camera works but kilopixels rather than megapixels. Each telescope is an independent sensor, and it contributes to the the big map. You might start with a grid of pixels and as the antennas drift into each box you measure the intensity of radio power, and write that number down in that box. Earth's rotation scans in RA already. so no matter where they are, the dishes should be evenly spaced in declination.
See answers to How did single dish (or single receiver) radio telescopes originally generate images?
Hybrid and other esoteric options
There is intensity interferometry but I don't understand it well enough to write authoritatively on it. It looks at fluctuations in statistical noise, and so you can probably get away with less critical timing; each dish would record the instantaneous power level at perhaps microseconds or even millisecond intervals. I haven't a clue how this works with arrays; I've only heard it used for two receivers, but you could certainly analyze it pair-wise. (see also Narrabri Stellar Intensity Interferometer)
You could also do something fun/interesting with pulsars, but I don't know what exactly.

Intensity plus Doppler frequency can sometimes give you distance if you  have a model; this is an early radio map of neutral hydrogen in our galaxy from  Why the blank wedges in this very early 21 cm map of the Milky Way? (Oort et al. 1958)
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