Here, we investigate, through parametrically optimized macroscale simulations, the field electron emission from arrays of carbon nanotube (CNT)-coated Spindts towards the development of an emerging class of novel vacuum electron devices. The present study builds on empirical data gleaned from our recent experimental findings on the room temperature electron emission from large area CNT electron sources. We determine the field emission current of the present microstructures directly using particle in cell (PIC) software and present a new CNT cold cathode array variant which has been geometrically optimized to provide maximal emission current density, with current densities of up to 11.5 A/cm$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ at low operational electric fields of 5.0 V/μm.