Maybe don't spend XP until you get the new pack?
Yep, this is the obvious solution. When you play the last scenario of an expansion, you record your XP. When you buy the next expansion (in that campaign), I would imagine you will be able to buy enough of the new cards to keep the deck new and fresh each time you play.
Plus we need to assess how much experience is gained in between scenarios. If it's 1 or 2 points, then swapping out cards would be problematic, if it's 4 or 5, then affording a new card would be feasible.
Then:
a) if we make some street math of a possible expansion pack, we have 60 cards. Remove 34 (let's say) for the new scenario, 26 remains. Each card comes in 2 copies, so, we have 13 new cards / pack, that are split between 6 spheres (5 proper spheres + 1 neutral), and must cover also the new "levelled up cards". This means each sphere will get 2 new cards / pack, and possibly they will be both stronger versions of existing cards, or they will be one new card and one powered up old card. So, if you really need that single card, you should have the experience to pay for it.
Additionally, scenarios can be played stand alone. And you can introduce the house rule that new 0-level cards coming with exp packs can be swapped in for free when you get that pack and move to the new scenario. It's much better thematically considering the RPG like atmosphere of the game and the idea of campaign play to have rules forbidding players to rebuild entirely the deck from adventure to adventure. It'll also probably mean that scenarios are not built with specific decks in mind, so, we won't be getting a Carrock or Rhosgobel situation in AH LCG