Using the MLE to sign Ty Thomas and then trading Perkins for a wing player
(1) Rondo + Ariza + Pierce + Ty Thomas + Garnett
(2) Rondo + JR Smith + Pierce + Ty Thomas + Garnett
(3) Rondo + Harden + Pierce + Ty Thomas + Garnett
Or use a portion of the MLE on Amundson/Amir, the remainder on a reserve player, and trading Perk for a wing player.
Love the ideas, but I doubt Perk's enough to haul any of those guys. And I'm almost positive that Ty Thomas will net more than the MLE. Consider that Darko netted a 3 year/21 mil deal after 3 years riding the bench and one mediocre year with Orlando. Tyrus' per 36 averages with Charlotte are 16 and 10 with about 2 steals and 2 blocks. His mid-range game has also improved pretty dramatically (his J looks better than Baby's did last year). And he's 23, absurdly athletic and has no injury history.
I think the only way we could land Tyrus Thomas is in a sign-and-trade for Ray, or, if Larry Brown's need for Sheed and MJ's alma mater fetish are directing personnel decisions in Charlotte, Rasheed and our 1st round pick.
Ray Allen at 9 mil per for Tyrus Thomas (at about 8 per for 2 or 3 years) + DJ Augustin would suit me. The Bobcats have a pretty sizable hole at the 2-guard when they play Gerald Wallace at the 4 (they've been playing Flip Murray and Larry Hughes a combined 38 minutes a game!), and a perimeter scorer like Ray would do wonders for their anemic offense.
Sign Mike Miller and you'd have a pretty nice team: Rondo-Miller-Pierce-Thomas-KG, with Augustin, TA, let's say Bobby Simmons, and Perk off the bench. That's a solid rebounding team, a good-to-great transition team (two 3-point trailers and 2 bigs who can beat their counterparts up the floor), a versatile defensive team and stronger half-court team (Thomas more of a threat than Perk with his jumper and lesser turnover rate).
Doubt Doc/Danny are as eager to acquire TT as we are, else they would have made a play for him when Chicago was shopping him.
As for Perk, I think your original idea of trading him to Utah for a late lottery pick is worth revisiting to facilitate KG's move to the 5. There are some excellent or at least intriguing 4s and 3/4s in the late lottery. Ed Davis, Al-Farouq Aminu, Patrick Patterson, Damion James, Hassan Whiteside, Ekpe Udoh, Greg Monroe and Stanley Robinson could all go somewhere in between 6 and 15. There are a couple of Euro bigs I haven't seen who show up in that range on the draft sites as well.
I'd also look into trading Perk for Thabeet to take advantage of Memphis' illusions of proximity to playoff contention, and gain the best of a potential-for-present trade. Thabeet's shot-blocking ability and potential as a finisher and rebounder put him a ways ahead of Perk as a long-term prospect.