Nothing about Gamble, in any way, is about "overturning the Double Jeopardy Clause". The Double Jeopardy Clause is for the protection of defendants, not the government. In the history of never has the government ever argued that their prosecution violates the Double Jeopardy Clause. Because expanding the Double Jeopardy Clause would help defendants, it would be rather unique for conservatives to support the notion. In fact, the obviously non-conservative RBG has stated in a previous case that the separate sovereign issue should be revisited (along with Clarence Thomas) http://www.abajournal.com/news/article/october_term_2018
Conservatives would be much more likely to want to deny (and the Solicitor General is arguing that separate sovereign prosecutions are fine by them) Gamble's petition and rule that it's not a violation of the Double Jeopardy Clause to have successive prosecutions. As a criminal defense attorney of 27 years I believe Gamble's position is beneficial to criminal defendants. It is a complete stretch to try and apply the issue presented in Gamble to presidential pardons.
Ultimately, the Conservatives and their tough on crime stance should support keeping things the way they are and preserve the status quo. The attempts to argue that Gamble would grant some additional power or scope to the presidential pardon is misguided. Daniel Richman, a Columbia Law professor, posits that state and federal charges usually have "no overlap, or almost no overlap, that would ring Fifth Amendment chimes in the absence of the dual sovereign analysis", and so the impact of overturning the separate sovereigns doctrine would be minimal. https://www.law.com/newyorklawjournal/2018/07/02/upcoming-scotus-case-could-complicate-ny-effort-to-close-double-jeopardy-loophole/?slreturn=20180902013459
So to answer the portion of your question that appears to be of most importance to you.....I don't think it makes a difference who the new nominee would be because I see nothing to support that Conservatives have taken the position that separate sovereign prosecutions are a bad thing.
(I apologize for the rambling response..... Seriously sleep deprived)
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