If you're trying to remove contaminating RNA in your preps, a simple RNase treatment should suffice, I think. Run two lanes on your gel, with and without RNase treatment and see if there are any changes in smearing/dodgey bands.
if it's low levels of RNA that you're trying to visualise, your best bet is to use SYBR Gold. It's more sensitive to single-stranded oligos than ethidium and has a very short staining time (5-30min). Adding too much ethidium on your gel can cause a lot of background fluorescence when visualising as well. Note that the SYBR Gold emission spectra is different from Ethidium Bromide as well so you might need a different filter on your imaging dock to see SYBR Gold-stained samples.
If you have too much EtBr, it could increase the background levels to make it hard to see your band of interest. I agree the both SYBR gold and GelRed are good alternatives to EtBr for RNA.