A computational design of linearly extended multiple resonance (MR)-type BN molecules based on DABNA-1 is proposed herein in the quest to find potential candidates that exhibit a negative singlet-triplet gap (ΔEST) and a large oscillator strength value. The impact of a proper account of the electron correlation in the lowest singlet and triplet excited states is systematically investigated by using double-hybrid functionals within the TD-DFT framework, as well as wavefunction-based methods (EOM-CCSD and SCS-CC2), since this contribution plays an essential role in driving the magnitude of the ΔEST in MR-TADF and inverted singlet-triplet gap compounds. Our results point out a gradual reduction of the ΔEST gap with respect to the increasing sum of the number of B and N atoms, reaching negative ΔEST values for some molecules as a function of their size. The double-hybrid functionals reproduce the gap with only slight deviation compared to available experimental data for DABNA-1, ν-DABNA, and mDBCz and nicely agree with high-level quantum mechanical methods (e.g., EOM-CCSD and SCS-CC2). Larger oscillator strengths are found compared to the azaphenalene-type molecules, also exhibiting the inversion of their singlet and triplet excited states. We hope this study can serve as a motivation for further design of the molecules showing negative ΔEST based on boron- and nitrogen-doped polyaromatic hydrocarbons.