I've actually thought of a similar idea to the one mentioned above, but I agree that the mountain wouldn't be able to sustain a major retrofit, mainly because it's not really a show building so much as it is an impressive bit of set dressing around a rapids track.
Based on the space available and the design of the land, the only way I would see to feasibly do a mine cart coaster would be to retrofit parts of the Grizzly River Trail (extended queue), Redwood Forest Challenge (main queue), and Mermaid/Wine Country (the gravity building/mine part of the attraction). I personally don't see those sections of the land ever being removed in the near-term, but the performance corridor is becoming less relevant as Mermaid ages poorly and Pixar Pier encroaches on the remaining sections of Paradise Garden Park.
The image below is messy, sorry, but it shows what I had in mind. Firstly, I don't want to seem like I minimizing the scope here, this is a big project, bigger than building a coaster from scratch on a green-field site by quite a bit. So it's not proposed here because it's easy or efficient effort/cost-wise. It's proposed strictly as a way to use the acreage DCA has in a denser way. GRR takes up a huge chunk of the park and many guests have no interest (in getting soaked). And even Anaheim has seasons, so it's a questionable use of that much space alone, I think.
There may be many logistical hurdles I'm not aware of or accounting for, so take this as just fun armchair Imagineering that is founded on the main strategic point:
DCA needs a themed coaster.
Okay, again, the image is rough. But here's what it tries to show: I overlaid a plan-drawing of Grizzly River Run onto a Google Earth image to clarify that ride's layout. Then I pasted Seven Dwarfs on top, it's outlined in teal and pink. Why two colors? Because I cut it apart and rotated each side a little differently and connected them with the solid teal lines. That would be the coaster...so a bit longer than Seven Dwarfs.
The blue shape about where the pickup truck is now on the trail is where a two-story queue building and coaster loading would be. The queue would use the north half of the trail (the south half may be needed for ride maintenance, not shown).
The yellow dots show the support posts for the coaster, and how they do not fall where the Grizzly River is. But, the rockwork and topography of Grizzly River would need to be significantly "modified." We saw Disney do some of that with the top of Splash Mountain -- cutting away and reworking old rockwork. Well, they would be doing that across the entire 4-ish acres of Grizzly River to put footings for the coaster everywhere they need to be. Like I said, it's a big project! Maybe as big of a project as that Fast & Furious coaster at Universal Studios Hollywood
(to squeeze in coasters, they gotta do what they gotta do).
