Are you using LabVIEW as the controller, non-controller, or both?
NI-488.2 does have a configuration option to enable unaddressing. I am not sure of where it is in LabVIEW, but if you search for unaddressing, you should find some information on it. With unaddressing, NI-488. will unaddress the device after communicating with it.
If you are not using LabVIEW as the non-controller, National Instruments does have a software package called NI-Device that may help. This is an API designed for non-controllers. It does not currently have a LabVIEW interface. It works under C++ with a PCI-GPIB board.
A third option is to rewrite your device application. Your device should really not care about TACS or LACS as you read them from the status register Your device
should only look for LACS, DCAS, and perhaps DTAS (if you desire triggering). When it is LACS, it should read data. After a read has completed, it should interpret the data and get ready for a response. It is only at that moment that the device should look for TACS (and DCAS). It is hard to put a flowchart here, but if you design the flow of a standard instrument, you will see some patterns about when to look for certain status bits.