Presumably there are two possibilities regarding powering the DRLs? Either they feed off existing DRL feeds which are non-LED based (does the GT have a non-LED DRL light? I actually don't know!) - if this is the case then a resistor will need to be added to emulate a non-LED light on the circuit. If not the case, then the solution ought to be even simpler: run a direct feed off one of one the 12V sources (such as cigarette lighter) to the DRL light and put a toggle switch on the underside of the steering column - the switch will be invisible (not interfering with design aesthetics of the interior) and easy to operate independently.
I say all this from an complete ignorance of how the existing GT headlights work. However I have installed LED DRLs on my pre-facelift 2007 QP and the latter option is how I have mine set up.
The auto shop I used is now defunct but I could try to find the companies the techs moved to if no one else has any installer recommendations.
With these cars and their 'touchy' electronics I would definitely only go to someone who has worked on modern Masers though...