Not sure Dooling can only be signed for $2.7m - haven't seen that, but have seen his cap hold is closer to $4m.
Per Larry Coon's CBA FAQ:
"If a team is over the cap and re-signs its Larry Bird or Early Bird free agent with a raise greater than 20%, in order to trade the player in a sign-and-trade arrangement, then the player's outgoing salary for trade purposes is either his previous salary or 50% of his new salary, whichever is greater. The team receiving the player always uses his new salary."
Dooling made $2,246,400 last season. A 20% raise of that is $2,695,680, or approximately $2.7 million. He can be paid more, but unless we start paying him $5.5 million for a season, $2,695,680 is the most his salary can count for in a trade. That's where this number comes from.