There are quite a few anti fungal essential oils.  In my experience, none
work exclusively and thoroughly on nail fungus.  However, it may be that
you'll want to add a few drops here and there to augment your treatment. Not
sure the body / fungus acclimates to treatment but adding 2-3 drops (yes,
drops) of any one essential oil to your mixture and then changing off every
week might be of benefit. Most if not all on my list below contain phenols.
Phenols are antiseptic chemicals, stimulate the body, beneficial in small
doses; large doses can be a poison to the nervous system and other body
systems.

Again, make sure they're diluted to .1% or less of total volume--hence the 2
drops in an oz. or two of your iodine/DMSO mixture. [note: Some essential
oil MLMs advocate the use of neat - undiluted - essential oils. While very
effective in treating a variety of maladies, it is the path to
sensitization--not a pretty picture.]

Extra virgin coconut oil is noted for it's anti fungal properties.  I
wouldn't count on it to eradicate a foot/nail fungus but I would use it to
prevent one, once you've cleared it up.

Essential Oils

Tea Tree (Melaleuca alterniflia)
Cedarwood, either
Atlas<http://www.naturesgift.com/essential/descriptionc-d.htm#CEDARATLAS>or
Virginia<http://www.naturesgift.com/essential/descriptionc-d.htm#CEDARWOODVIRGINIA>
.
Lavender (Lavendula vera, Lavendula angustifolia
Lavendula officianalis)
Lemon Eucalyptus *Eucalyptus
citriodora*<http://www.naturesgift.com/essential/descriptione-g.htm#LEMON%20EUC>
Myrrh (Commiphora myrrha)
Tagetes * Tagetes
glandulifera*<http://www.naturesgift.com/essential/descriptions-y.htm#TAGETES>
oregano *origanum vulgare*
thyme *Thymus vulgaris*
clove  *Eugenia carophyllata*
**Lemongrass *Cymbopogon Citratus*
sage *Salvia officinalis*
lemon myrtle*Backhousia citriodora*
Fragonia™ <http://www.naturesgift.com/essential/Fragonia-Essential-Oil.htm>

research references
//www.naturesgift.com/antifungal.htm
//nail-fungus-treatment.blogspot.com/
//antiagingchoices.com/Aromatherapy/healthy_nail.htm
//www.essential-oil-recipes.com/essential-oils-chemistry.html
//www.health-oils.com/antifungalessentialoil.html
http://www.deancoleman.com/essentialref.htm#eucalyptus
http://www.essential-oil-recipes.com/aromatherapy-essential-oils.html
//antinailfungus.com/toenail-fungus/essential-oils-cure-toenail-fungus
//www.squidoo.com/toenailfungushometreatment
//www.aromaweb.com/essentialoils/default.asp
//www.healingnaturallybybee.com/articles/anti1.php
//www.healingnaturallybybee.com/articles/anti6.php
//ezinearticles.com/?Powerful-Essential-Oils-Kill-Nail-Fungus&id=2238