What are the diameters of the strings you are using ?
Those gauges are way out of whack - .042 and .030 are OK but you want anything between .020w and .024w on the top. You can go plain gauge, but I find them rather stiff and dead sounding compared to a wound of the same gauge. We produce various sets, all aimed at proper playability - getting the string gauges right can make a huge difference to the feel of a guitar.
so you used the #5, #4, and #1 strings from a pack...with the #1 drop tuned a Major 6th to get the higher G note, yes it will feel floppy.
1) try the #3 string instead for the octave G
2) or the #2 string since its only a major 2nd drop tuning for that octave G
3) or tune the #1 up another octave so its uptuned a minor 2nd for a 1-5-16 (8-octave) tuning. don't worry, a light tension string can be tuned up a 4th and becomes a medium tension string.
I rarely look at if the pack says light or medium because the string gauges vary quite a bit from one brand to another and from electric to acoustic. I always look at the actual gauge of the strings. The ones mentioned by CB John are perfect for GDg tuning but I often use lighter ones for a different sound and feel. The lightest gauge I've gotten away with for the high g string is a .017 plain. It has plenty of tension and bends well if bends are in your playing style. The low G is .036ish and the middle D is around .026 when I want a lighter set. This closely corresponds to an electric "regular" set's 5th, 4th and 3rd strings if that helps.
.040, .030 - unwound .014-.018 . I like the unwound high string ,