Is there a conventional way of searching for lands in a mono-red deck?
Solemn Simulacrum is good colorless fetch (and draw).

Traveler's Amulet and Horizon Spellbomb can get lands into your hand.

Caged Sun will get you lots of mana (but no lands) as will Koth of the Hammer.

Iron Myr is a good mana producing creature

Infernal Plunge and Geosurge can also have their uses.

Fiery Fall is the only mono-red card that could be considered land fetch but it's not Standard.

Other non-Standard methods for increased mana in red can be:

Extraplanar Lens

Gauntlet of Power 

Gauntlet of Might

Mana Flare