It is not hard to find a scoring profit. Look for type 3 single star solar systems. Planet IV always has two moons. The base costs 25 score points x1000 +5181 maintenance says look for total greater than 164. To have it Last 25 turns at a scoring and maintenance profit look for 164+75 = 239. Of the 13 such systems in my homespace on map6 there were six really good ones - Ute@246, Vote@303, Equal@343, Eural@278, Sop@306, and Ebb@283. Combined 1759 * 184 per turn minus 6 * 5181 is a minerals profit starting at 292570. In 25 turns it drops to 1309 * 184 - 6 * 5181 = 209770. Since the scoring for bases is 25 * 6 = 150 then I am still making a scoring profit on the set of 59k and would not need to scrap for another few turns. My profit over base maintenance for the least of them would continue for 246 - 3N = 29 makes N = 72 turns by which time the game will be OVER because it is already turn 47 and the soonest I can do this is about 55.
As I said before it only makes sense if you need your score to remain below MEE while getting a boost in minerals, and do not do it if you expect to get the proper atmosphere race any time soon. In my case both are true.