I don't see the error rate published anywhere....they mention in their FAQ that it could be 5% for freshwater tests, but that doens't help us a whole lot.
Based on the no algae thing and stagnant, way-high N thing (in spite of bio-pellets), I'd presume you're too low on P.
Start dosing P up to ≥0.10 ppm, but keep testing NO3 and make sure you don't drive it below 5-10 ppm in the process.....the more P you add, the more active the reactor will become, so watch carefully! I'd still be decommissioning the reactor by removing the pellets little by little while the dosing is going on.
The tank should be fine at these nutrient levels going forward....if you choose to take them lower,
do it slowly. Better than going lower is to let algae grow and keep a healthy crew of grazers on top of it......just long enough to grow a bomb crop of corals that will
displace it.
A refugium or ATS has certainly proven useful, but I still don't know if I'd say necessary.....but if you wanted more than just alga+grazers, then one of these would be the way I'd go....whatever seems to be the least work for you. (Algae + grazers has to be the absolute least work since you're not involved except at the planning and feeding stages – but use whatever works!)