I guess the obvious answers are to either supply a much higher current initially, to bring the capacitor voltage up to the measurement maximum voltage quickly, then switch to the final current to do the resistance measurement, or avoid using a resistance measurement circuit to measure a capacitor!
The first option isn't ideal either because when you switch to the final current to measure the resistance, the capacitor may have to discharge, which will also take time.
Are you trying to measure the leakage current of large capacitors? If so, you should have said so at the start. You'll always get a useful answer more quickly if you don't play guessing games.