The modern synthetic tracking technique (ST) can make use of small and medium-sized telescopes to detect asteroids fainter than the classic blinking methods, by arbitrary shifting and co-adding more images of the same survey field, if GPU computing resources are available. In the framework of the Romanian ParaSOL project, we developed and tested an innovative ST algorithm capable of detecting in near-real-time very faint near-Earth asteroids (NEAs), which likely became the first ST pipeline developed in Europe. To test our pipeline, we conducted several mini-surveys using three large-field telescopes, namely the ING's INT, the Korean KASI and the Brazilian T80S telescopes. Most images were processed using our Umbrella Image Processing Pipeline (IPP) module. The ST search was conducted using our Synthetic Tracking via Umbrella (STU) module and the commercial Tycho Tracker software, which allowed to compare and complement the findings. The source validation was supported by reducers using our new Webrella platform. Most of the nights were reduced in near-real-time, demonstrating the ability to process, sort, and report large volumes of data. We discovered 5 credited and 4 one-night NEAs, co-discovered other 3 NEAs and recovered 3 poorly known NEAs. We flagged 59 NEA candidates for recovery and orbital classification, discovering, co-discovering and recovering other 18 orbitally related NEAs, additionally improving the orbits of 23,428 known asteroids and reporting 1,374 unknown objects. A comparison between ST and traditional blinking detection using the new EURONEAR tool MagLim shows improvements of two magnitudes and a two-fold increase in the number of detections. A preliminary comparison between STU and Tycho shows that STU detects about 70% of Tycho findings, however STU detects rapid objects much faster than Tycho, 7 NEAs with speeds between 2-10‧‧/min being found exclusively by STU. Based on our surveys, we assessed the current NEA discovery rate using 1-2-m class telescopes and ST methods, finding that one NEA candidate can be discovered in every 9-12 square degrees up to magnitude ∼23.