You can't just throw a wire over the balcony with an internal tuner like 
that.  That sounds like an end-wire which those tuners won't handle.  I 
don't think the 570 has the range of some of the earlier Kenwoods like the 
850.

I'd suggest that you try getting a real tuner, you could save money in the 
long run.  You can find some decent tuners used.  You'll need a way to read 
SWr.  You can use a VCO hooked across the meter if you don't have an 
accessible watt meter.

Apartment antennas are a significant compromise, no matter what you have, so 
don't expect to win DX pile-ups.  But, there are some stealthier ways you 
can get things to work.