The structural question you're circling has two distinct layers, and they're getting conflated in how you've framed it.
The GP entity for deal one is already formed and already carries whatever liability exposure that deal generates. Dissolving it does not eliminate that tail. The obligations travel with the entity through the wind-down period and, depending on jurisdiction and how the operating agreement is written, can follow members personally in certain circumstances. Dissolution is a process, not a shield. A licensed attorney needs to walk you through what the actual tail looks like on a closed deal in your specific structure.
The separate question is whether deal two should use the same GP entity or a new one. Most experienced sponsors I've seen discussed in the forum keep a management company or GP holdco as a persistent operating entity, the thing that holds the brand, bank accounts, and relationships, and then either (a) use that entity directly as GP across deals or (b) form a deal-specific GP LLC in which the holdco owns the interest. Option (b) gives you cleaner liability ring-fencing between deals at the cost of more entities to maintain. Option (a) is simpler but means LP two is looking at an entity that also bears exposure from deal one.
The assumption doing the most work in your question is that keeping the first entity alive is the expensive choice. The real cost question is whether a thin, dormant entity creates false comfort. If the liability from deal one can reach the entity used for deal two anyway through common ownership, separation at the GP-entity level may be less protective than it looks.
The $50 to $300 annual maintenance cost is genuinely not the variable that should drive this decision.
What does your current operating agreement say about GP liability to the partnership versus to LPs directly?