Implication One: Difficulty
Adding attack and defense values into how saves works affects the difficulty of many kinds of monsters.
Soldiers and monsters that are higher level than the party will be harder than in the normal system: they will have an easier time shrugging off save-ends effects the party puts on them, and the party will have a harder time shrugging off save-ends effects the monsters put on them. This is because soldiers & monsters above the party's level tend to have better than average attack and defense values.
Likewise, brutes and monsters that are lower level than the party will be easier: they tend to have lower attack & defense values, and so they'll have a harder time shrugging off the PCs' effects and the PCs will have an easier time shrugging off their effects.
While this is hardly an insurmountable problem, it does mean that the DM will have to be a bit more careful in balancing encounters.
Implication Two: Book-keeping
Saves are fairly easy to keep track of in the normal system: the DC is always 10, there are relatively few modifiers to keep track of, and those modifiers almost never change over time for a given effect. Despite that, at high levels it's still a fair amount of book-keeping to keep track of all the save-ends effects flying around.
In your system, you not only have to keep track of more modifiers, but those modifiers change every turn thanks to the cumulative penalty. You also have to remember the DC, since it's the target's defense rather than always being 10.
Implication Three: Sources
In the current system, if a player or monster has
ongoing 10 fire damage (save ends) on it, and something else applies
ongoing 10 fire damage (save ends), then the effects don't stack, and you just ignore the new instance.
In your new system, you'll have to decide how to handle it if two different sources put the same save-ends effect on a target. Is the new source or the old source responsible for making the attacks (they might have had different attack values or save penalties)? Does the cumulative penalty for successful save-attacks reset?
What if the source falls unconscious or dies? Does it continue making the save-attack rolls?
Implication Four: Conditional Bonuses
The part about repeating the attack with any modifiers it had when the attack was first made makes conditional bonuses much more valuable when using attacks that inflict a save-ends condition.
If they're inflicting a powerful status effect, players will go to greater lengths to get combat advantage, any bonuses their leader can hand out, etc. This in turn will make nasty effects tend to last longer.
Implication Five: Attack/Defense Debuffs
Effect that debuff attack or defense values become much more powerful. Debuffing a target's attack value also makes any save-ends effects it causes less dangerous. Debuffing a target's defenses also makes it harder for the target to shrug off any save-ends effects on it; save-ends penalties to defenses will be particularly nasty.
Remember that this will also make violating a defender's mark less attractive for monsters with attacks that cause save-ends effects.
Personally, if I was a player in a group that implemented this system, I would rebuild my character for attack & defense penalties ASAP.
Implication Six: At-Will Save-Ends Effects
Monsters with an at-will save-ends attack (most common in controllers and solos) make the difficulty and book-keeping problems much more severe.
Players with an at-will ability that inflicts a save-ends condition (yes, there are ways to get this) will become more or less viable, depending on their stats and how they inflict the condition.
When you say you want the system to take into account the strengths and weaknesses of combatants, I envision simply adding some extra penalties and bonuses.
You can adjust for level difference by simply giving monsters +1 to all saves for every level they have over the party's level, or -1 to saves for every level behind the party they are. The other thing that pops into my head when you say strengths/weaknesses is elites and solos, but they already have a bonus on saves (and outright immunities to many effects on a lot of the solos from MM3 & later).
You might also apply a monster's save bonus as a penalty to saves PCs make against its effects, but I would be very careful when trying this out: many enemies, especially controllers and solos, can put out a lot more save-ends effects than a typical PC can.