SIM900 SMS timestamps are not accurate enough
As @PlasmaHH suggested, changing the text mode to PDU mode (using AT+CMGF=0) did give me some more information. The parsed PDU string now contains a property udh which has some more information about the message. If it's a message consisting out of multiple messages it will tell me how many parts there are and what part this message is of the total message.

udh: {
    length: '05',
    iei: '00',
    reference_number: '4E',
    parts: 3,
    current_part: 1
}