We demonstrate over 3 kV gate-pad-connected field plated (GPFP) $beta$-Ga$_2$O$_3$ lateral MESFETs with high lateral figure of merit (LFOM) using metalorganic vapor phase epitaxy (MOVPE) grown channel layers and regrown ohmic contact layers. Using an improved low-temperature MOVPE selective area epitaxy process, we show that a total contact resistance to the channel as low as 1.4 $Omega$.mm can be achieved.The GPFP design adopted here using PECVD (plasma-enhanced chemical vapor deposition) deposited SiN$_x$ dielectric and SiN$_x$/SiO$_2$ wrap-around passivation exhibits up to ~14% improved R$_{ON}$, up to ~70% improved breakdown voltage (V$_{BR}$ = V$_{DS}$ - V$_{GS}$) resulting in up to $sim$3$times$ higher LFOM compared to non-FP $beta$-Ga$_2$O$_3$ lateral MESFETs. The V$_{BR}$ (~2.5 kV) and LFOM (355 MW/cm$^2$) measured simultaneously in our GPFP $beta$-Ga$_2$O$_3$ lateral MESFET (with L$_{GD}$ = 10 $mu$m) is the highest value achieved in any depletion-mode $beta$-Ga$_2$O$_3$ lateral device.