Think you trade Cousins, cut Hunter and cut Pierce. Hunter because he's hurt all the time and Pierce because he's somewhat replaceable. That gets them $39 million under the salary cap. You then draft Linderbaum at #12 and sign a RG. Use the rest of the draft to fine CB, LB, DL, OL. Sign a QB, or if the new regime likes Mond, go with him, but I doubt it.
Maybe they can grab Uwazurike, Rose, Kolar and Purdy and make my head explode.
The need DL and Uwazurike might fit at either DE or DT in the future. They will need LB with Barr leaving, so Rose would be a great fit. I don't think they can afford to sign Conklin, so Kolar (or Allen) makes sense.
Hope they can re-sign Xavier Woods, then their Safeties are solid with him, Smith and Bynum.
CBs are a huge question mark. Would have Dantzler, Boyd and Hand on contract. Boyd and Hand could each save nearly $1M on the cap if cut, though.
LB is weak after Kendricks. Maybe Blake Lynce or Chazz Surratt step up.
DT would still have Tomlinson, Lynch and Watts, plus a wildcard in Twyman.
DE would be down to Wonnum, Jones and Robinson, so big question marks.
If you draft Linderbaum, you've got the makings of a really solid OL. O'Neill and Darrisaw at tackle, Linderbaum at C and Cleveland at LG. Maybe Wyatt Davis figures it out at RG, or you sign someone new. Maybe Bradbury could play better at guard? I don't know. Either way, you are stuck with him.
I'd consider trading Mattison, if you got something good for him. He's got one year left is all and I bet he gets a bigger contract, so he'd be leaving eventually.
Here is a proposed Vikings draft - cyclone blinders on later rounds

1st Round - Linderbaum. If he's gone, maybe you go with with Kenyon Green (OL) from A&M or Nakobe Green (LB) from Georgia
2nd Round - Edge rusher - Jermain Johnsone from FSU or Travon Walker from Georgia
3rd Round - best available CB, LB, Edge
5th Round - Mike Rose
6th Round - Chase Allen
6th Round - Enyi Uwazurike
6th Round - Brock Purdy
7th Round - Andrew Mevis