I use Audacity for some recordings and also have a Beheringer mixer that I use.
First off you may want to think about trying a different mic as each voice is suited to different mics and settings. Try different makes and models till you find your fav.
Control is very important and a lot of singers have poor mic technique. Here are some tips.
Do not sing too close to any mic as it will pick up lots of distortion and breathing noises especially on the big notes.
I cringe when I see so called pros on TV kissing or trying to eat the mic and holding their fingers over the grill.
Use the mic as a volume control by varying the distance it is from your mouth. Closer for low quiet notes and further away for the more powerful or high notes. Just move your head back or forward to vary the distance. Never put it to your lips keep at least 2-3 inches away.
Always record dry with no effects from your Beheringer. It is easy to add and alter these FX post record but impossible to remove if the recording has them already and are set wrong.
You say you use an amp and then feed that signal into your desk. Can you not just plug your mic straight into the mixer or is this a pre amp. Using an amp first could be your prob.
It is so difficult however to give best advice as I really need to see and hear your setup to accurately see what is needed and adjust settings.
Plane fares from Edinburgh to Michigan are so expensive. LOL

Re Audacity there are different versions available I use a couple. In version 1.2.6. there are some interesting settings on Gverb that can give good effects rather than just echo or delay. However the settings have to be played about with till you get what you are looking for. The most important parts are the room size and the amount of dry signal left unprocessed it is expressed as a percentage. I tend to put that setting fairly high it sounds more natural. The room size should be set not too large usually about one third up the scale. A good tip is to use low settings which can be repeated or gradually increased till you get what you want.
Very important... When setting up the record level make sure it is set very low otherwise the signal is too harsh and will have lots of hiss. You can always amplify a weak signal after recording.
Final tip save often so you have something to fall back on in case you completely mess up and use UNDO/REDO and repeat till you get what you want.