Sometimes, examining the result is more valuable than the rules and descriptions.
1. You can use Astral Projection to avoid the Wish penalty
This opens up the possibility of a smart NPC or Player getting away with a lot more than they otherwise could. However, both are 9th level spells, and cannot be cast by the same individual in the same day by normal means. Either two characters of at least level 17 must work together, or one character will need to have a way to duplicate one of the two spells. There are no Astral Projection items given in the DMG, and all Wish items have limited uses. Other phenomenon to duplicate one or the other spell will be incredibly rare.
Therefore, if you rule that this combination can successfully bypass the penalty, it will be difficult to perform as an individual, and probably impossible to do regularly. A pair of high level characters working together becomes the only way for this to happen often.
Is this okay to allow once in awhile? What are the story implications of an NPC doing this once or twice, using very rare and legendary magical items? This could be a great setup for a plot or entire adventure. If a Player does it, does it actually break the campaign, or just change it?
What would a pair of such high-level NPC characters look like? What would be their motivations for working together, and how did they discover this exotic loophole? Would they use this often, or save it as a last resort option?
Would a pair of such high-level PCs even need this combination to achieve their goals, or can they use other means? What do their companions think of this? And again, does this actually break the campaign, or merely change it?
What entities might take notice of such a thing, particularly if performed multiple times? How do these entities react?
Rather than denying an interesting combination of magics or skills, it could be more fun to tackle the implications to the story and world.
2. You cannot use Astral Projection to avoid the Wish penalty
One must then ask the question: Can you use Clone or Simulacrum to bypass the penalty? I'd argue that if Astral Projection doesn't work, then neither would Clone, but Simulacrum would be a separate question entirely, as the created creature is a different entity with its own stats and not tied to the original's life force. Granted, the simulacrum could only cast Wish once, but there is nothing to say the same wizard couldn't create multiple simulacrums across different days, allowing this combination as many times as desired. And one casting of Wish can be pretty damaging all by itself.
If one could not bypass the penalty using Astral Projection, would characters in the world even know that? It is a very specific set of circumstances, and could lead to disastrous experimentation on the part of NPCs or Players alike, with little chance of finding such an esoteric interaction pre-recorded prior to making the attempt. There are good storytelling opportunities here as well.
3. You can use Astral Projection to avoid the Wish penalty, but suffer other effects
Perhaps the backlash damages the character's silver cord. Perhaps it reverberates back to the magical item used to create this combination of spells, breaking or corrupting it. Perhaps it rips a hole in the Astral Plane, or causes a huge psychic storm, or results in a Wild Magic Surge with the power of a Wish spell behind it. Perhaps the effect of the wish mysteriously ends as soon as the Astral Projection spell ends, or it prematurely ends the projection spell and makes it harder/dangerous/impossible to re-enter the Astral Plane.
This third option is how I would rule it. Why limit your selection to "yes, this can happen" or "no, it cannot"? The world is grey, and much more interesting because of it. Let the Player(s) do it, with unforeseen consequences beyond just "some deity somewhere is aware of your presence and does not approve". Have NPCs in your world cause these consequences when they try. Let this absurdly powerful combination of magics tear at the seams of reality in unpredictable ways. Embrace the changes that occur to the campaign, and let it make your adventures as DM and Players all the more exciting.