Not very helpful, Charlie...
Beamin, first, let's see which of the Grundigs you have - model number, please.
Most portables, particularly here on the East Coast, won't take too much antenna to cause problems with overloading, especially if you're near a major metro area, where hearing FM and TV stations (sometimes referred to as 'breakthrough') can cause major hassles.
Your idea about a random loop is sound, but living in an apartment is going to present challenges in trying to get a LOT of wire out, quite apart from using a portable. In addition putting antennas inside will almost certainly increase the amount of noise from local sources (and there are so many...) from inside the building.
If you have access to an attic (I did for many years...) you have many more options. Don't worry about getting a quarter wave of wire up - at 3 Mhz, that's roughly 80 foot (the common formula is 234 / f(mhz) where f(mhz) is the frequency in megahertz), and that would be a tough call in a small apartment.
If you can get the parts (or have a good junkbox) to build it, I'd highly recommend the Carpet Loop. It uses 4 or 5 conductor cable, which is quite easy to find at Lowe's, etc. This design allows the loop to be as small or large as you want - usually the loop is created by stringing around the perimeter of the room. I was lucky when I built mine (I had a pretty decent junkbox) - I had a 25 foot square (roughly) attic I could play with. At 100 foot, my RX-320 heard all sorts of stuff I never would have with just a crappy piece of wire strung around the room. Here's the article and schematic...
The Carpet Loop -- antenna special on hard-core-dx.com
A little more detail about your situation is in order here...Mike