Astral Projection is not weaker than Plane Shift, but is a non-combat spell
For all this, if you are homebrewing something, you can only do so if your DM agrees to it. So, if you are not the DM, talk to your DM about it.
I do not think that swapping the spells would create a large enough power shift to require extra Ki costs and Ki restrictions to balance the change if you keep the casting time to an hour, to not change the nature of the feature from a non-combat one to a combat one. If you don't keep the casting time, your suggested change looks OK to me.
Detailed explanations follow.
Astral Projection is a 9th level spell. Plane shift is only a 7th level spell. Spell level normally corresponds directly to how powerful the spell is, the higer level, the more powerful. The rules even tell us so (PHB p. 201):
Every spell has a level from 0 to 9. A spell’s level is a general indicator of how powerful it is
While the level of spells does not match their relative power in all cases, unless something is quite wrong with the assigned levels of those two spells, swapping them out should not make you more powerful.
What are possible reasons Astral Projection is higher level than Plane Shift?
Travel to any outer plane. The first reason is that you can travel to a plane with plane shift if and only if you have the right tuning fork for for it. That is not a given at all. It is entirely dependent on your DM. Travling to the Astral Plane on the other hand is entirely in your power, and by the workings of that plane should enable you to locate the color pool you need eventually, and allow you to go where you want. The DMG is pretty explicit on p. 46 that obtaining tuning forks for Plane Shift along with the spell is not expected:
Plane Shift. The plane shift spell has two important
limitations. The first is the material component: a
small, forked, metal rod (like a tuning fork) attuned to the desired planar destination. The spell requires the proper resonating frequency to home in on the correct location, and the fork must be made of the right material (sometimes a complex alloy) to focus the spell's magic properly. Crafting the fork is expensive (at least 250 gp), but even the act of researching the correct specifications can lead to adventure. After all, not many people voluntarily travel into the depths of Carceri, so very few know what kind of tuning fork is required to get there. [Emphasis added.]
Protection from death. Secondly, while there are ways you can get killed while traveling in your astral form (e.g. psychic wind or a lucky hit from a Githyanki sword), this is still a lot less dangerous than traveling in person. That is extremly valuable on the Astral Plane itself, where you get a free "avoid death" ticket rolled in with your travel spell.
From the spell text, it appears Astral Projection does not extend this protection once you arrive on another plane, because the spell says it pulls your body there. However, it is not entirely clear if you really die on an outer plane if you traveled there by Astral Projection -- there is text in the DMG that indicates you would not, expanding on the spell text (DMG, p. 47):
A character's death-either in the Astral Plane or on the destination plane-causes no actual harm.
There are only a few cases where the DMG adds additoinal rules to a spell (Phantom Steed is another), and this is one of them. That means, if you would die or not on another plane is at least up to your DM. Not dying certainly would help to justify the two levels higher placement of Astral Projection. For context, this is also how the spell worked in earlier editions of the game.
Shenanigans. Lastly, and again somewhat depending on your DM, there may be some shenanigans you can pull with Astral Projection, like immmortality by not aging.
How relevant are the downsides of Astral Projection?
I agree that in some regards, Plane Shift seems better than the higher level Astral Projection, and the two level gap is maybe a bit questionable.
Offensive use. For starters, you can use plane shift offensively, to shift away an opponent. You could not do it here though, as you only can affect yourself, so this does not matter.
Casting time: Astral Projection takes an hour, instead of an action, and leaves your body behind, so you cannot use it in a combat situation as an escape hatch, the same way you can use Plane Shift. I think this is actually the largest downside, as a "get me out of here" effect is quite powerful to gain access to, turning the feature from a non-combat one, to a combat one. Instead of increasing the Ki cost, an option to balance this could be to extend the casting time to an hour, when you cast the Plane Shift with this feature.
Transition period. Lastly, if your goal is to go to any other plane than the Astral, and you already have a tuning fork, and your DM rules you would die there normally, then Astral Projection would just add a period of travel and of needing to protect your normal body. That is not so big of a downside. If your party does not travel along with you, they should be able to protect your body. If they cannot, you still can set up a sanctuary somewhere from where to cast the spell. After all, to get that feature, you should be 18th level, with access to many powerful friends and resources.
Overall, even with these downsides, I do not think it would be justified to conclude Plane Shift is an overall stronger spell, and needs additional compensation on swapping it for Astral Projection. But there is a large influcence in how your DM treats the various aspects of it, and I think there is a risk of changing the nature of the feature into a combat one, which I as a DM would try to avoid.
If you do want it to be combat relevant, then your suggested restrictions would seem reasonable, so you can not shift twice in a day before reaching 20th level, keeping the uses of plane shift balanced to what a wizard could do.