There's a few things I can think of that might mitigate the problems you're worried about.
The writers of the original Planescape setting seem to have foreseen the problems you're worried about, and included some countermeasures in the rules themselves.
First, most magic items come from a very small number of places: The Prime Material Plane is a big manufacturer of magic items, and so is the Outlands. Most of the other planes, however, are not: The Inner and Transitive Planes are either too environmentally hostile or poor in resources for magic item creation to be widespread, and the Powers who make their kips on the Outer Planes tend to be leery of allowing magic weapons and armour to be stockpiled without a blessed good reason. There are exceptions, of course (certain powers of artisanship and magic actually encourage magic item creation, and the foundries of the City of Brass are legendary) but in the scheme of things, these don't make much of a difference: There's a high chance that every magic weapon and item of armour in the party came from a very small list of places.
Second, even if a magic weapon loses bonuses due to not being on its plane of origin, those bonuses still count for the purposes of overcoming damage reduction. As far as I can tell, the canny bloods who scribed the Planescape knew that having magic items be affected by travelling between planes would cause cannon problems with earlier adventures that didn't mention those effects, so they wrote in this rule specifically to make the effect of bonuses being lost so subtle that players (and characters) could plausibly have not noticed it. More importantly for your purposes, it means you can slip up and apply the wrong amount of bonus every now and then without straining the credibility of the setting: Even if the +1 light mace your fighter bought in the Cage shouldn't get that +1 when she's in the Abyss, it can still smash a vrock's beak if it hits one.
Taking those two together: There won't be as much paperwork generated by magic weapons and armour as you expect, and it won't matter too much even if you make the odd mistake. (A player or two might tumble to the idea of getting a magic item made in a particular place specifically in order to get around the penalty. This is a good thing: If they care that much, then they shouldn't mind keeping track of their bonuses themselves.)
Divine casters are generally nerfed on the Outer Planes, yes. (On the Inner, Transitive and Prime Material Planes, no clerics of any power take penalties due to distance.) There's three ways around the penalties, though.
First, clerics who follow a cause rather than a specific deity can simply ignore the whole issue. Personally I like to follow a deity when I play a cleric, but that's a matter of personal taste.
Second, only clerics whose Powers have set their divine realm on an Outer Plane are affected. There's a fair few elemental powers with realms on the Inner Planes for obvious reasons, and there's even a few who've established realms on the Prime; Their clerics can go anywhere on the planes and not have to worry about how far it might be from their deity's doorstep.
Finally, there are a vast number of powers - mostly neutral, but also of other alignments - who have placed their divine realms in the Outlands, and the great thing about the Outlands is that it's conveniently close to everywhere: It's only one step, maximum, to any other outer plane, and so only a -1 level penalty, max, to be faced by those powers' clerics - and of course, outside of the Outer Planes, there's no penalty at all.
Admittedly, the above options do limit the list of deities available to players who want to avoid penalties, but still, it should give you some options. (Incidentally, the reasons why people are clerics in the Planescape setting are the same as they are in any other setting: Because they Believe in their deity, and because they Believe that serving their deity is worth it. I suspect you knew that, though.)
Other suggestions for mechanics are off-topic for this site, I believe. Unless you want to describe a specific problem they should address?