Does EthBr turn restriction enzymes into nickases?

I'm looking for a way to create a nick at a specific point in a closed circular plasmid, to see if increased DNA flexibility facilitates DNA uptake. New England Biolabs now sells specific nickases, but their site preferences aren't very convenient. I also have an old paper (Shortle et al. 1982 PNAS 79:1588) describing use of ethidium bromide to convert restriction enzymes into nickases. So I think I'll just do a simple test. Here's the relevant paragraph from that paper:

Restriction Enzyme Nicking Reactions. Covalently closed circular pBR322 DNA was nicked with restriction endonucleases HindIII, Cla I, or BamHI by incubating 10 pkg of plasmid DNA in a 100-Al solution of 20 mM Tris HCl, pH 7.8, 7 mM MgCl2, 7 mM 2-mercaptoethanol*, gelatin* (100 Ag/ml) and a concentration of ethidium bromide (50 ug/ml, 75 ug/ml, or 100 ug/ml, respectively) determined by titration to give an optimal level of nicking. An amount of restriction endonuclease was added sufficient to convert 50-90% of the input DNA to an open circular form on incubation at room temperature for 2-4 hr. The nicking reaction with the EcoRI enzyme consisted of 100 mM Tris'HCl, pH 7.6, 50 mM NaCL, 5 mM MgCl2, gelatin* (100 ug/ml), ethidium bromide (150 ug/ml). Reactions were stopped by addition of excess EDTA followed by phenol extraction and ethanol precipitation.

I have lots of supercoiled plasmid that has one EcoRI or BamHI or HindIII site, and a big bottle of 1 mg/ml EthBr. So I'll just set up a series of digests with different concentrations of EthBr and restriction enzyme and the standard digestion buffers*, and run a gel to see what I get.

*In the old days we used to add mercaptoethanol and gelatin to stabilize our restriction enzymes, but I won't bother.