Unless I'm misunderstanding your screenshot, you're not actually pumping out of the liquid tank, you're splitting your output from the crucibles into both the tank and the geotherms. Is that correct? If so, that's a likely culprit. Also, as mentioned above, that lattice of pipes you have above the geotherms is keeping the ones on the far side of the input to get filled. Go directly from the machines into the the tank, then from the tank to the geotherms. Also, using liquiducts will transport the lava faster, and allow you to have multiple input lines to the geotherms, as they don't connect to each other unless you specifically connect them with a wrench.
Oh, and yes, I'd probably use at least 3 engines per crucible. Good catch, Mero.