Simple, 'Toss the most recent NN mbxs into the air & let Automatic Mailbox Provisioning redistribute them onto new dbs' script

move-MailboxesMostRecent.ps1

<# -- TRIMMED GIST -- SEE FULL SCRIPT AT GITHUB FOR DETAILS
https://github.com/tostka/PowerShell/blob/master/ExchangeScripts/move-MailboxesMostRecent.ps1
-#>

$domaincontroller="DOMAINCONTROLLER" ;
write-verbose -verbose:$true  "$((get-date).ToString('HH:mm:ss')):Using BatchName:$($BatchName)" ;
write-verbose -verbose:$true  "$((get-date).ToString('HH:mm:ss')):Moving most recent $($Number) mailboxes" ;

if($db=get-mailboxdatabase $database -domaincontroller $domaincontroller ){
    write-verbose -verbose:$true  "$((get-date).ToString('HH:mm:ss')):Moving most recent $($Number) mailboxes" ;
    if($mbxs = (get-mailbox -Database $db.identity -DomainController $domaincontroller)) {
        if($showdebug){write-verbose -verbose:$true  "$((get-date).ToString('HH:mm:ss')):($($mbxs.count) raw mailboxes returned in db)" };
        $mbxs = ($mbxs |sort whencreated)[(-1*$Number)..(-1)] ; 
        if($showdebug){write-verbose -verbose:$true  "$((get-date).ToString('HH:mm:ss')):($($mbxs.count) net mailboxes subject to move)" };
        write-verbose -verbose:$true  "$((get-date).ToString('HH:mm:ss')):Filtered most recent mailboxes $($mbxs.count) returned" ;
        $BatchName="ExMoves-db-$($db.name)-REBAL-$(get-date -format 'yyyyMMdd-HHmmtt')";
        write-verbose -verbose:$true  "$((get-date).ToString('HH:mm:ss')):BATCHNAME:$($BatchName)" ;
        foreach($mbx in $mbxs){
            "==$($mbx):" ;
            write-verbose -verbose:$true  "$((get-date).ToString('HH:mm:ss')):WHATIF:$($whatif):Moving Mbx:$($mbx.alias):$($mbx.displayname):$($mbx.whencreated)" ;
            $spltMove=@{
                identity=$mbx.alias ;
                BadItemLimit=100 ;
                AcceptLargeDataLoss=$true ;
                suspend=$true ;
                batchname=$BatchName ;
                domaincontroller=$domaincontroller ;
                whatif=$($whatif) ;
            } ; 
            if($showDebug){Write-Verbose -Verbose:$true "$((get-date).ToString("HH:mm:ss")):Executing New-MoveRequest with settings:"; $spltMove|out-string } ;
            New-MoveRequest @spltMove ;
        } ; # loop-E
        if(!$whatif){
            write-host -foregroundcolor green "$((get-date).ToString('HH:mm:ss')):MOVEREQUESTS STATUS, BATCH:$(BatchName):" ;
            Get-MoveRequest -BatchName $BatchName -domaincontroller $dc | ft -auto DisplayName,Status,TargetDatabase;
        } ; 
    } else {
        throw "NO MATCHING MAILBOXES FOUND IN DB:$($DATABASE)" ; 
    } ; 
} else { 
    throw "specified db $($database) not found" ;  
} ; 

<# -- TRIMMED GIST -- SEE FULL SCRIPT AT GITHUB FOR DETAILS -#>