How to build a two-world wargame

The main hook of Illeria is that the battle takes place in two worlds - the physical and spirit world.  Each character has two bodies, one in each world (I use the term "dopplegangers" to mean the body in each individual world, and "character" to mean the entity that is made up of both dopplegangers).  I've always had two goals:
1) The worlds should feel linked;
2) The worlds should feel different.
Actually implementing these goals has probably been the hardest part of making this game.

I have had many failed ideas for how to implement the two-world system, including:
-Each character can only act with one dopplegangers per turn.  This didn't work because it led to players abandoning one world entirely so they could have all of their characters focus exclusively on the other.
-The rules of each world were basically the same, but the abilities would seem more mystical and surreal in the spirit world; for example, a physical-world summoner would summon animals, and a spirit-world summoner would summon demons or elementals.  This didn't work because the underlying rules were so similar, so the differences in abilities felt like a different shades of the same thing, rather than different things.
-There is one board, and physical- and spirit-world dopplegangers were both there, though they mostly only interacted with dopplegangers of the same the same world; for example, spirit-world dopplegangers cannot attack physical-world dopplegangers unless they have a special attack.  I didn't like this one because it felt too much like there was just one world.  
-Characters who had a power in one world gave their doppleganger in the other world a bonus; for example, if a character's physical-world doppleganger was a melee fighter, then their spirit-world doppleganger would get a bonus to its aim.  This was okay, but my playtesters often complained the worlds didn't feel connected enough.
-There were several abilities which affected both worlds, such as a melee attack that damaged both the character's physical-world and spirit-world dopplegangers.  This might have worked if most of the abilities were like this, but these kinds of abilities are weird and hard to come up with.  As a result, the majority of abilities didn't have direct between-world effects, so the link felt too weak.  

Here is what I've landed on, at least for now.  My underlying concept is that the physical world in the source of life that everything is anchored to, but the spirit world is the source of magic and power.  So, I have the following:
1) Dopplegangers in the spirit world have all of the magical powers (e.g. spells, summoned creatures, exploding archery attacks, melee attacks with status effects).  Dopplegangers those in the physical world have few powers at all, and they aren't super interesting (e.g. simple archery attacks, stat boosts).
2) Characters can become "linked" by having their spirit-world doppleganger capture some part of the battlefield.  If a character is linked, its physical-world doppleganger gains the abilities of the spirit-world doppleganger (e.g. if the spirit-world doppleganger can throw lightning, then the physical-world doppleganger can too if the character is linked; otherwise the physical-world doppleganger has no special powers).
3) The physical-world and spirit-world dopplegangers have different baseline stats.  The physical-world dopplegangers are slower, have less health, and are more susceptible to magic attacks, but are better armored.
4) If a spirit-world doppleganger dies, then the character's physical-world doppleganger becomes weakened, and becomes highly susceptible to magic attacks.
5) If a physical-world doppleganger dies, then the character's spirit-world doppleganger takes damage every turn until they die too.
6) If a character is linked, a physical-world doppleganger can use its action to heal its spirit-world doppleganger.  
7) If a spirit-world doppleganger dies, but the character's physical-world doppleganger is still alive, then there are ways to revive the spirit-world doppleganger.
8) The game winning conditions always occur in the physical world.

I think when I tried #1 and #2 for the first time, it gave me this real sensation of, "This is it, this is what I've been looking for!"  All together, I think that these produce a distinct purpose and feel for each world.  The spirit world feels weird and fantastic (see #1).  The goal of the spirit world is not too win per-se (see #8), but rather to empower your characters in the physical world (see #2).  The physical world feels much less mystical (see #1), and like the source of power is really coming from elsewhere (see #2).  However, actions on the physical world feel more impactful (compare #5 vs. #4), both because they are permanent (see #6 and #7), and because this is ultimately where the game is won and lost (see #8).  And, the differences in baseline stats (see #3) seem to cause abilities to function slightly differently in each world (e.g. I found that a swarm of weak monsters were more damaging in the spirit world, because the characters are generally unarmored).  So, like I said, I'm really happy with what I currently have.