re: Construct a realistic playoff team under the following criteria.

Absolutely can: Grant is an Unrestricted free agent.

Under terms of the current CBA, sign-and-trades come with many significant restrictions. Transactions under this rule require all of the following to be true:[2]

The player must re-sign with his former team.
Additionally, the player must have been on the team's roster at the end of the immediately previous season. This provision, introduced with the 2011 CBA and maintained in the 2017 CBA, closed a loophole that allowed a team to sign-and-trade any player to whom it held "Bird rights", regardless of whether the player was active in the league.[a] An example of such a transaction banned under the current CBA is the Dallas Mavericks' inclusion of Keith Van Horn in the trade for Jason Kidd in order to match salary.
While restricted free agents can be signed and traded, this is not allowed if that player has signed an offer sheet with another team.
The team receiving the player cannot have a payroll that exceeds the so-called "apron"—a designated level above the NBA luxury tax threshold—after the trade. A team with a payroll above the apron can only receive a player in a sign-and-trade if the transaction drops that team's payroll below the apron. Once the transaction is complete, the team receiving the player is hard capped at the apron for the entire season.
The receiving team cannot have used the so-called "taxpayer mid-level exception" in that season. The taxpayer mid-level exception is a limited financial buffer that teams with total payroll above the luxury tax threshold must use to sign players for up to 3 years.
The regular season has not yet started.
The player must receive a contract of either 3 or 4 years (not including any option years), where only the first year must be fully guaranteed. (5-year sign-and-trade contracts were abolished in the 2017 CBA to disincentivize the transaction.) In turn, this means that he cannot be signed using a salary cap exception that does not allow the team to offer a 3-year contract.