I would try fixing the problem at its source and not try to put a band aide over a gushing artery. If you do not want it to sound artificial or degrade the sound, you need to fix it at its source.
Your Problems can be one, two, three, four, five, six or any combination or all the above. Its up to you to troubleshoot it and find out what is wrong.
1.) Electrical (bad ground??)
2.) Bad Guitar Amp or the setting on your guitar amp is not viable for the sound you are going for
3.) Maybe the amp is cannot do what you want.
4.) Bad chords/cables
5.) Bad recording technique
6.) Using wrong mic for that situation
I can record chords with reverb without any noise form all my guitar amps and so can thousands of others, so i'm pretty sure you will be able to troubleshoot this and solve your issue
CJ