Trade all 2nd round picks + 24th for a higher pick (#17?). Trade 3rd pick in a three-team trade for picks 14 and 15. Now we have four decent successive draft picks.

Pick up Jerebko's option. Decline Johnson's option. Let Zeller walk. If Sully actually demands anything like the 15 million we've heard about in the media, let him walk too. If he accepts something like 8 million, then keep him. Similar decision-making process with Turner (if too much, let him walk). In all likelihood, these guys will be able to get big offers from other teams with more cap space and a more desperate need for decent players, and we need the roster space. I'm assuming that we ultimately let them walk too.

That's Johnson, Zeller, Sully, and Turner all gone with four newly drafted players coming in.

Here's where things get wicked weird:

Trade Bradley and Mickey for Robin Lopez. We have assets. I don't know what Lopez is worth but he seems to be a slightly above average center. Bradley is young and they need a good guard like him. I'm guessing we give up three future second round picks on top of Bradley and it'll work out.

Trade James Young and a future second round pick for Marco Belinelli. He had a terrible year with a terrible team and his price will be low but we know he can shoot.

Offer Batum a maximum contract. Offer Ezeli whatever we can afford. We shouldn't have to overpay but we should have room for a very good offer.

Based on the most recent mock drafts (not the one OP linked), we could be taking the following guys in the draft: Deyonta Davis, Timothe Luwawu, Denzel Valentine, Domantas Sabonis.

So, now we have the following lineup while only having given up future second round picks:

PG - Isaiah Thomas, Marcus Smart, Terry Rozier

SG - Marco Belinelli, RJ Hunter, Denzel Valentine

SF - Nic Batum, Jae Crowder, Timothe Luwawu

PF - Jonas Jerebko, Deyonta Davis, Domantas Sabonis

C - Robin Lopez, Festus Ezeli, Kelly Olynyk