Sorry you feel slighted. I regularly listen in that vicinity and I have never heard anyone rejected for using a "rice box" rigs. Many of the modern rigs have excellent quality when properly adjusted.
One of the first things I was taught as a Novice was that if anyone ever says you have a major problem with your signal stop transmitting until it is fixed. Don't even transmit to close. *shrug*
In general terms here are things to look at:
-Read and follow the radio manual
-One thing often not understood is that AM uses about four (4) times the power of SSB. Consequently you will probably find you manual says to limit power to perhaps 20w or 40W.
-Your first reaction when told you were over modulating should have been to reduce ALC as needed until you got a clean report. If that was not a enough, reducing Mic Gain would be the next choice. Of course Compression or Speech Processor should never be used.
-If you are serious about AM operation, then building signal sampler and using an O-scope will help keep things tamed. In the mean time, get with an AM'er or technician in your area who can confirm the right settings for your radio.
There are plenty of resources on the net for AM.
Good starting point: http://amfone.net/Amforum/index.php
Don't give up, and keep it clean!