After days of trying I finally got myself Solgaleo in a Beast Ball (1.45% catch rate with Lvl. 3 Power Catch Sandwich, minimum health and paralysis), with an Impish nature and the "alert to sounds" characteristic, matching Nebby's personality. Was only really possible because I farmed 100 Beast Balls back when the Smeargle glitch was still a thing.
Now unto Lunala... I'll try to get a Nature + Characteristic combo that's not the same but conveys the same thing, like Naughty + "Impetous and Silly", but with them 1/750 odds to get a specific Nature + Characteristic I can't really be too picky. I really don't get why they disabled Synchronize this generation even for static encounters.