We report a fully-correlated multi-mode pumping architecture optimized for dramatic noise reduction of a class-A dual-frequency Vertical External Cavity Surface Emitting Laser (VECSEL). Thanks to amplitude division of a laser diode, the two orthogonally polarized modes emitted by the VECSEL oscillating at 852 nm are separately pumped by two beams exhibiting fully in-phase correlated intensity noises. This is shown to lead to very strong and in-phase correlations between the two lasing modes intensities. As a result, the phase noise power spectral density of the RF beat note generated by the two modes undergoes a drastic reduction of about 10 to 20 dB throughout the whole frequency range from 10 kHz to 20 MHz and falls below the detection floor above a few MHz. A good agreement is found with a model which uses the framework of rate equations coupled by cross-saturation. The remaining phase noise is attributed to thermal effects and additional technical noises and lies mainly within the bandwidth of a phase-locked-loop.