If you want to continue to use T7 and IPTG induction without re-cloning add 1% glucose (final) to all of your plates and media, this will reduce the levels of polymerase made in DE3 cells and also block your T7 promoter if it is also lacO. Induction by IPTG will not be affected so you should get roughly the same induced levels of expression. For toxic proteins this simple step can make the difference between expression or cell death!
As Paul suggested there are other E.coli strains that produce lysozyme as a natural inhibitor of T7 polymerase (we routinely use Rosetta (DE3) LysS).
I have used pLys in the past but it is an additional plasmid you must select for and I have seen much lower overall protein using that system. You can also use site directed mutagenesis to reduce the strength of your T7 promoter. I abolished leaky production in my system via this method. It will also reduce the overall total protein but no additional plasmids are needed. I have a paper in review now relating to this. If you want more details send me an email. [email protected]