Yes, you can use astral projection from planes other than the Material Plane. The Manual of the Planes describes how spells that access transitive planes such as the Astral Plane function on other planes in the section "Moving Among Transitive Planes" (starting on page 45).
Characters generally must use spells or spell-like abilities to access a Transitive
Plane. ... the astral projection spell takes you to the Astral Plane ... Such spells should function in any location coexistent with or coterminous to the plane.
It includes various examples of travel between transitive planes on page 46. These examples reinforce that "Material Plane" is a placeholder and that you can use astral projection from anywhere that is connected to the astral plane. Your body will be left behind on the plane you project from.
From the Ethereal Plane to the Astral Plane: You can move to the Astral Plane from almost everywhere on the Ethereal Plane, because the Astral Plane connects to everywhere on the Ethereal Plane. ... If you're using an astral projection spell, your physical body remains in the Ethereal Plane ...
From the Plane of Shadow to the Astral Plane: From the Plane of Shadow, you can use the astral projection spell, leaving your body behind on that plane ...
As you have said you are willing to consider Spelljammer rules, I can pull a few quotes in for you that might help clear this up.
From Spelljammer Core Rules: Book 2, Concordance of Arcane Space, p. 17
Clerics in Space: A cleric may not regain spells above 2nd level while in the phlogiston. This is because he remains out of direct
contact with his deity.
A cleric who enters a foreign crystal shell is similarly restricted.
The only exceptions to this occur when a cleric's deity (or a similar
power) is recognized in the foreign shell or the cleric casts a
successful gate spell, affording his deity access to the foreign
shell.
Any god or power is considered "recognized" within a sphere if he has
worshipers and/or an organized church anywhere within that system.
This does not mean that a PC cleric can move into a shell and
automatically establish a base of worship for his god. For a deity to
be a recognized power in any shell, he has to have an established
base of worshipers somewhere in the system.
Additionally, the same rulebook adds the following spells on page 22
Contact Home Power (2nd level Conjuration)
The user of this spell establishes a tenuous link through the Astral
Plane between his present location and that of the power he venerates.
This link permits the priest to regain his spells as if the god is
recognized and venerated within the sphere.
The duration of the spell is one week, as long as the cleric remains
in the same crystal sphere in which he cast the spell. Passage into
another plane (even the ethereal) will break the spell.
and
Detect Powers (2nd level Divination)
[This spell] allows a cleric to determine if there are friendly gods
and/or other powers within a crystal sphere so that he may recharge
his higher-level spells within its borders. It also reveals if the
god(s) revered by the cleric are worshiped within that sphere.
In this case 'friendly' is defined as 'same basic attributes and portfolio' or possibly 'same god by a different name.' As two examples...
-Paladine and Bahamut are the same god, but known by different names and roles in two different spheres.
-Reorx and Moradin are two distinct gods (from Krynn and FR respectively), but they are sufficiently similar that a cleric of one could receive spells from the other.
So, if you take these pieces of information into account, it gives you the following answer:
When you are on a different world within the Prime Material Plane, you may only regain spells up to 2nd Level unless
1: Your god has an established base of worshipers on that world, or on another world within the same Sphere. This implies that the other gods in the system don't actually get a direct say in the matter...though they could certainly stamp out 'heretical religions' if necessary.
2: You use Detect Powers to locate a friendly deity (or your own) and refresh your spells via them.
3: You use Contact Home Power on a weekly basis to 'phone home' and keep that connection open so you may reload your spells.
4: You use Gate to connect directly to your deity's domain and refresh your spells from them directly.
Now, I do not have access to the Planescape books, so I am not 100% certain that this isn't contradicted somewhere in those books...but if you are willing to abide by Spelljammer rules, that's how it works.
Best Answer
Deities basically never come to the Material Plane. When they do, it has huge ramifications for that plane as well as for the Outer Planes, and that tends to cause lots of problems and anger all the other deities.
Instead, they send avatars to the Material Plane—and even that is quite rare, because even that still causes a lot of trouble. Most of the stats for “gods” in the books really are for their avatars. You can even find different stats for the same deity in different books, because really both are just avatars.
Slaying an avatar, anywhere, probably disrupts a deity’s plans for that avatar, and it takes the deity a year to make another one. It definitely does not result in the deity’s actual death.
In the case that a deity is actually physically present in the Material Plane (or anywhere else, for that matter), then death does mean death. Or, at least, nothing seems to say it doesn’t—deities are outsiders, outsiders can die, ergo death. Deities & Demigods does suggest that when making your own pantheons, it is up to you to decide whether or not gods can actually die, but we know that D&D gods usually can die so that would only apply to custom settings.