I was thinking about it some more, and I think the issues I've got with the colony crises in its current form does come down solely to how it ramps up too quickly. If each crisis you triggered slowly increased in strength, then I think it would work out a lot better. Say you had a 'colony level' that increased each time you successfully defeated or resolved a crisis. This colony level determines how strong both the actual crisis event is, and how strong random fleets spawned around your colonies are. It might also unlock increasing benefits for you and your colonies, like increased colony and administrator limits. Maybe this is where all the old colony management perks go?
Pure speculation and brainstorming past this point:
Say at level one colony level, only Pirates, Pathers, and the Hegemony can take an interest in you. Random fleets that spawn around your system range from small to medium sized bounties during the early game (four frigates to a couple destroyers with escorts). You have a colony limit of 1 and an administrator limit of 0. The first colony crisis triggers at 200-250 points and is a single large bounty fleet (a 60-100 DP fleet which might include 1 capital and/or 2-3 cruisers). Defeat the expedition/raid and you get a colony level up. Going over your colony limit will give a big increase to the rate that colony crises spawn, letting players accelerate that if they want to level up their colony level fast. Or just put AI cores on everything.
Getting to level two colonies means you get 2 colony slots, 1 administrator slot, can now negotiate to resolve a colony crisis once it triggers, and can draw the attention of all the factions. This would also be where the Luddic immigration mechanics would be enabled. Random fleets hovering around your systems are now larger and more common. The crises fleets will now include multiple fleets, with the exceptions of the Hegemony and PL who follow different rules. It's at this point where defeating a faction crisis will also permanently disable that crises and earns the respective bonus for doing so.
Each time you defeat or resolve a crisis increases your colony level, which also increases the difficulty of the next crisis. This way they prove they can handle defending their colonies against a larger force. If they fail, they keep the current colony level. Again, with the exceptions of the Hegemony and PL. The two largest factions must be defeated at their full strength in order to disable them and earn the benefits for doing so. If the player gains their attention before they have their endgame fleet, they should probably accept the downsides of failing the crisis or make a deal with them rather than fighting the full strength of those factions.