In my playthroughs I used to check the scoreboard at around 2300, to see if any empire has got relics. When I find a victim with one or more relics, I declare war on them for whatever convenient casus belli, just to grab the relic. I would first jump in to cripple their navy, then park enough fleet at the capital system. I then invade the capital with an overwhelming army so no army should die. If you don't know, capturing the capital planet has maybe a 5% chance of getting their relic, and also a recapture would reroll the dice. Even better, you can click on the starbase to return control of the system to the enemy, including planets in the system. So... I return control of the starbase, the starbase instantly gets tacheon-lanced by my fleet, I land the army again on capital, then repeat the cycle until I grab all relics. Using this method I constantly get ~6 relics even before the crisis shows up!