I don't find current Lifestone to be out of the balanced area, as you say, and it's ok for me (both using it, and facing it).
With this - "bad design, because it allows players to pay morale for material advantage" - I don't agree. It is exactly the kind of trade-off you would expect such game to allow, and make you decide about. Direct win condition / measure (morale) vs indirect / investment into potential. Are material sacrifices for tempo, position, later material advantage, checkmate, all bad designs in classic chess ? Should rules include we can only trade same things, eye for eye ? Not even taking things for free would be allowed :) . King vs King end game tends to have predictable outcome in classic chess, so you would have to either checkmate from equal material, or manage to promote pawns for any material advantage. Wouldn't that make great design :) .

Now evaluating the proposed change of LS (against current):

• Only allows me to have "improved quality" of revived piece by 3 value vs army limit (current - 4/5/6/7), worse.
• I don't gain "extra" champion slot, worse.
• Before activation, inactive slot is champion (vs minion slot in current), worse.
• Costed / costs me (in army building, and in match while LS doesn't translate to power on field) more in morale, worse. On the other hand, it doesn't cause the extra pay penalty, better. But, I only pay penalty for current when / after it provides me the advantage I want it to give, not beforehand. Could be seen as "2" (sort of) morale penalties vs 1 in favor of current, worse.
• It can move by itself, tier 3 swaps could even be usefull themselves at times, better (with possible extra upside on tier 3).

Current seems better as sum, and is better in categories / comparisons that make you decide to include LS in first place. Imo, you don't include LS because it maybe escapes from threat, or maybe uses swap before reviving champion. You do it for the extra champion it provides + "extra quality" compared to invested cost (army building).

When comparing to other existing pieces, the suggestion for new LS takes it a bit into direction of Patience.