It was a H&K, but a rather old model.
Isn't the GMG a bullpup? Those aren't used in the danish military.
And the machinegun, well since it let the cartridges falls directly down it was no problem with me being lefthanded. In fact I rather liked it as I found the secondary hand to be more of a problem to place (you had to hold the weapon on the stock quite far back), also it kept the weapon firmly in place while I reloaded (beltfed). The only problem arised when I had to change the barrel, that could be done singlehanded if you were righthanded, but not me, I had to let it go completely (as most did), but again the difference was marginal, a second or so added to the three seconds perhaps (those old MG42s have really nice short changetimes for their barrels).