Right now, I'd project the opening day lineup to consist of Sano at 1b, Polanco at 2b, Simmons at ss, Donaldson at 3b, Arraez in LF, Buxton in CF, Kepler in RF, and Garver catching. Assuming a 13-man position player active roster, that leaves 5 spots open. Ryan Jeffers is one. Jake Cave is another. At some point, sooner rather than later, Alex Kiriloff is a third. Brent Rooker is a fourth, leaving Lamonte Wade, Astudillo, Blankenhorn, Gordon to fill in (or rotate in) the final spot.
Once Kiriloff arrives, left field stops rotating, and while Cave is backup outfielder number one, having Rooker in the lineup (as well as Arraez, who is not great in LF, but his bat needs to stay in the lineup), tilts toward a second infield utility player being handiest. We can argue over who that should be (Astudillo as 3rd catcher, 3b, LF?; Blankenhorn or Gordon), but I'm sticking with my hopeful prediction of Gordon taking on that part-time skeleton key spot, offering some speed, flexibility, and reasonable pop.
The depth chart says that (after catcher), Rooker backs up 1B, or potentially Kiriloff or Kepler, with Cave getting an OF start; Arraez backs up 2b along with Gordon; Polanco backs up SS; Arraez or Polanco or Sano backs up 3b, depending on whether the team prefers keeping Jorge to a primary-2b, sometimes ss role or moves him around more.
Once Kiriloff arrives in LF, (or RF, if they want to shift Kepler to LF), there will be fewer ABs available for any outfield position reserves.
DH, then, rotates between a handful of players - Sano (Rooker plays 1b, or Kiriloff plays 1b with Cave/Arraez in LF), Donaldson (Arraez or Polanco plays 3b, the other plays 2b), Rooker, Cave, Arraez as DH with no substitutions needed, maybe Polanco with Arraez playing 2b.
While a Cruz reunion is favored by many, and for good reason (this is not to bash Nellie, who is a leader and great baseball player), none of the above is possible with a single, non-position-player taking on 500+ at-bats in the DH slot. There is a sound argument that Cruz's production would dwarf doling out 500 ABs between Rooker, Arraez, Cave, or whichever catcher isn't starting that day, but there's a logical argument that it wouldn't.
And then there's the money. I think the figures thrown around ($12M with incentives to $15-16) are a little light, and gobbles up all - or almost all - of the remaining budget. I don't pretend to know what that number is, and clearly the team isn't saying, but multiple reports indicate that the annual salary for Cruz would constitute the lion's share of it.
This team needs bullpen help and (in my opinion) one more starting pitcher for depth. We can hope against hope that Maeda, Berrios, Pineda, Happ and Dobnak all make 30 starts, but it never happens. We can hope against hope that Smeltzer, Thorpe, Duran and Balazovic can ably fill in, but that, too, walks a thin rope (and depending on how it shakes out, Thorpe could be lost from that depth chart if he doesn't make the relief corps). 8-9 starters is not enough, especially when two have never pitched a major league inning, and all are expected to throw 250% of their 2020 innings.
It is also noteworthy how close our top prospects are to reaching ML level - a glance at the MLB prospects list https://www.mlb.com/prospects/2020/twins/ reflects that no less than a dozen of the top 30 (those who haven't already appeared in a big league game) have "2021" as their anticipated date of arrival. I don't see a dozen spots opening up this year, but wouldn't it be nice that if Celestino pounds AAA, or Miranda or Larnach or Lewis, that we would have the ability to move pieces around to make that happen.
Our clearest open path to at-bats in 2021 is through the DH slot. The remaining 8 offensive starters seem pretty locked in (again, once AK moves to everyday play). The same dollars that bring us Cruz could fetch a couple of relievers (Colome, Rosenthal, Kennedy, Clippard?) and a starter (Brett Anderson, Jake Arrieta, Carlos Rodon, Cole Hamels?) who slip through the cracks.
One final point - I know the team will miss the homers from Eddie and Nelson, but this team too often sat around waiting for some player to hit a bomb. The playoffs the past two years only highlight that shortcoming. Improved flexibility throughout, better defense, room for promotion from prospects, and more reliance on 1-9 rather than solo homers, while beefing up pitching depth, seems a stronger formula for success in 2021 (and beyond).