I also did a transformation assay on the H.in KW20 strR cells that SS asked me to grow up and make competent earlier this week. Since it's friday (and I won't be in tomorrow), I'll have to ask RR to kindly take them out of the incubator for me.
Between experiments, I read a paper titled "A Role for Single-Stranded Exonucleases in the Use of DNA as a Nutrient" by Palchevskiy and Finkel (2009). They also used exonuclease knockouts (RecJ and ExoI sound familiar?), but to study viability, not transformation. When exonucleases are not present, DNA is not degraded, so it can't be used as food to nourish the cell, so the cell (eventually) dies.
Lastly, I'm currently making competent the H.in KW20 that was given dprA::spec DNA earlier this week. I'll check the transformation frequencies of this strain to check that they have indeed recombined dprA- DNA into the chromosomal DNA, then I'll probably extract this strain's chromosomal DNA and feed it to my double mutant RecJ-ExoI- cells in order to make a triple mutant.