After performing a few "Design of Experiments" (DOE) this is what is achievable using a print head that offers 96 DPI, roughly 10mil dots. All it all, this is workable.
Two factors, that will seem obvious are the distance between the print head and the paper and the second is the interval between ink jet pulses.
In the first test the distance was around 1.5 cm and the inter-pulse interval 800uS. In the image below the distance has been reduced to several mm and the inter-pulse period extended to 30 ms. Under closer magnification individual dots are visibly separated which would of course cause an open circuit. Note that as each trace changes direction there appears to be a widening at the apex of the line. Ideally, the ink should be dispensed based upon the true position of the ink head in relationship to the object, rather than assume a constant velocity that simply does not exist. No doubt, correct position based ink dispensing can be readdressed when the system is retrofitted with servos.
The present system is not going to get to 3 mil lines, but it certainly looks as if it might make 10. As a matter of reference, the vias are 30 mils. A standard poker chip would just fit within the board outline.
This DOE will have to be printed when the substrate is changed from paper to ceramic green tape, and the ink changed to one of the three I have been storing in the refrigerator.