Mr. Bill,
The kit you bought is intended for very low output and so very short distances. It is a simple design but may be subject to input overload from your audio source. A couple of input pots would easily eliminate that problem. Since the output circuitry is very simple, it is unlikely there will be an efficient coupling to your antenna making the range even shorter. I think Bluetooth ranges and coverage is likely what you will find.
When you wish to upgrade, take a look here...
http://www.ramseyelectronics.com/hk/....asp?page=amfm
I recently built an FM100B for the radio station here. Although it is likely an overkill for you, I really was impressed with the construction and coverage. Ramsey has been around for a while and I have built some of their Ham radio projects over the years.
I don't have a problem with zener diode circuitry if properly designed. However, in this application, the zener may introduce significant additional noise that will degrade the transmitted audio.