The Eco has two holes - the ventilation hole and a very small hole with two water droplets embossed on the plastic. That one, which I believe is the designated watering hole, is on the other side of the "bump" from the vent hole, sort of in the corner where the cord plugs in. You could easily get some narrow tubing through that one, or could temporarily do it through the vent hole.
Remember that eggs have to breathe. DO NOT try to compensate for low RH by closing that vent hole! It MUST stay at about half, and don't block it with tubing for more than a few seconds. Even in waterfowl, avoiding high CO2 (in other words, suffocating the chicks) trumps humidity.
Brinsea wants hatching at 65% OR HIGHER. So I agree, you need to get it up there, especially given that your extremely dry entry air (the stuff coming into the vent hole and being swirled around the eggs) is so extreme.
There are a couple of things that I would personally do (and, to let you know that I do have some experience, I have an Eco in lockdown right now and when I was getting my biology degree I was in charge of the embryology labs and had to get not just eggs but shell-less eggs all the way to hatching in our scientific incubators): My top choice would be to thread some tubing in and add water a few times a day. My second choice would be to just open the dang thing when the RH is starting to fall, pull out the sock, soak it in hot water and put it back in. Yes, you'll lose RH for maybe twenty minutes but a micro-dip is going to do less damage than hours or a day with too-low RH.
There are ways to set up permanent warm humidifiers that will blow water-saturated fresh air over them on a continual basis, but they require some equipment. Since right now I think you are looking to just solve the one problem, you may not want to invest the time or effort. But if there's one HUGE mistake you can make, it's closing or blocking the vent hole (and this goes for the styrofoam ones as well - never never raise the RH by closing the plugs). That should be avoided at all costs.