Overall champion status
From my point of view the champion respawning / champion build time increase will only mean my wife will be unhappy while she waits for her champion to respawn (as she doesn't like shared control) doing absolutely nothing in front of AI War ;-).
I do agree champion is extremely powerful as a unit, and I do agree the problem lies in the fact that champion power is completely separate from AIP increase, unlike normal player's operation (though I cannot imagine I - a normal player - could simply hunker down and wait till she hunts her nebulas; I'd die of boredom. It's always a joint operation, with engineers with cloaker, planet neutering etc).
I think the deep strike is too simple when you have a champion, especially now when you can repair a champion in the nebula (so no problem with "cloaker and 5 engineers generating deepstrike on enemy planet all the time to repair her champion").
The problem as I see it
The problem with the champion - for me - is the lack of "conflicting gauge", like AIP. Not the economy (though I don't mind it nerfed even if I usually have HORRIBLE energy problems).
A three-part suggestion
Anyway, my suggestions (more of a brainstorm than fully fleshed-out implementations). I have thought about them as a group of suggestions, not "A or B or C separately", but we are far less experienced in AI War than other posters in this thread, so feel free to modify them ;-).
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01 - If a champion is in game and deep strike takes place for more than 30 seconds (so it is not accidential), spawn an aggressive Nemesis. One per a short interval of time (3 minutes?) or something.
Reason: Champion is a perfect deep strike unit - swift, durable, incredibly efficient paired with raid starships. Let the opportunity cost of the Champion be the extremely feared Nemesis unit, which becomes a part of the threat fleet. In other words, if we want to raid the AI, we'd better have good defences in place. It's better to take one more planet as a base of operations (it can always be a Warp Jammer planet, or a highly defended world - the role of a normal player (in other words, me)).
If undefended, this Warp Jammer planet can fall and raid party in long range operations will become a deep strike. Then a player has two options: scrap the fleet, forfeiting the operation (with usual cost of losing fleet) or eat the deep strike.
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02 - If a champion enters a Nebula, spawn a retaliatory "Nemesis wave" which comes out of the Nebula.
Reason: As far as I read it, the problem comes from the fact a player can create a decent defense force and do nothing and a champion can enter Nebulas at will. So this is an action with no "AI reaction cost".
First 1-3 Nemesis waves should be quite simple, as Champion is quite useless before destroyer level, but 4th Nemesis wave (including Destroyers) could be quite dangerous for a single-planet player.
This, especially combined with deep striking, will force defending player to create a defence able to accomodate the new-found dangers.
If the Nebula planet is ours, normal player can prepare for this wave. Else, it might increase the Threat fleet.
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03 - Reduce starting knowledge (not Metal and Crystals, Knowledge) from 10k to 5k. Increase knowledge gain from planets from 3k to 3.5k.
Reason:
The parity with the current state shall be achieved at 10 planets (+200 AIP). Although at ~15 planets the total knowledge of a player will get higher (by 2500, which is about one knowledge raid), but 20 planets games are very different to low AIP games anyway (and are not the 'Low AIP 10/10 wins' which seem to be the core of an argument in this thread).
Lately (since I started playing AI War, somewhere about version 4) some things were made "always available", for example Cloaker Starships, Gravity Turrets etc. Some of those were earlier my 'mandatory' unlocks. For me, this means I can always afford to unlock both Harvesters Mk3 (as a first move) and expand to 5-10 planets total having everything I need for the particular game.
If I had only 5k knowledge, I would not "automatically" unlock harvesters - I would have to decide "Turrets? Harvesters? Mk2 ships? Starships? What do I need?". A choice would be back, situation-specific. I wouldn't be able to make "a decent enough defense" having 5k knowledge (3k -> fortress, oh, no harvesters to support the power loss) for one planet, I would NEED to expand if I wanted to deep strike with a champion or take fourth nebula.
That way I would suggest against reducing nebula resources / energy bonus, because with nebulas the cost would be present, one of Nemesis. And as the knowledge has been reduced, some expansion is mandatory.
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To sum up:
1 - Would influence only the games with Champion players (Deep Strikes when Champions present spawn Nemesis)
2 - Would influence only the games with Champion players (Nemesis wave spawns when Nebulas entered)
3 - Would influence every game, and this worries me a bit. This is, sadly, crucial for #1 and #2. Maybe Champions - Easy and Champions - Hard is needed?
Small bonus, please ;-):
04 - For the sake of everything holy (or unholy, as you prefer), PLEASE eliminate Distribution Node 33% chance for a resource drain.
If I pop one of those, I either need it (lost a fleet and desperately need to rebuild) or it is the start of the game and I don't want to wait. I'd prefer to have 2 AIP cost than to have 33% chance to lose resources instead of gaining them.