We present the construction and test results of Coils 2 and 3 of a 3-coil 800-MHz REBCO insert (H800) for the MIT 1.3 GHz LTS/HTS NMR magnet currently under construction. Each of three H800 coils (Coils 1-3) is a stack of no-insulation REBCO double pancakes (DPs). The innermost 8.67-T Coil 1 (26 DPs) was completed in 2016; the middle 5.64-T Coil 2 (32 DPs) has been wound, assembled, and tested; and for the outermost 4.44-T Coil 3, its 38 DPs have been wound and preliminary tests were performed to characterize each DP at 77 K. Included for Coil 2 are: 1) 77-K data of critical current, index, and turn-to-turn characteristic resistivity of each DP; 2) stacking order of the 32 DPs optimized to maximize the Coil 2 current margin and minimize its Joule dissipation in the pancake-to-pancake joints; 3) procedure to experimentally determine and apply a room-temperature preload to the DP stack; 4) 77- and 4.2-K test results after each of 64 pancakes was over-banded with a 75-μm-thick stainless steel tape for a radial thickness of 5 mm. Presented for each DP in Coil 3 are 77-K dada of critical current, index, and turn-to-turn characteristic resistivity.