The problem with high-salt (high electric conductivity) samples is heating losses due to coupling of sample with the coils. One way to reduce that coupling is to use smaller volume samples by using smaller diameter tubes. For example, this paper shows that NMR can be done in 3.5 M NaCl.
Another method is to use low conductivity buffer (e.g. HEPES) to keep ionic strength high, while reducing the losses to conductivity.
Maybe you can benefit from shimming on lineshape of some small molecule - like 3-(trimethylsilyl)propane sulfonic acid (TSP), with better shims water suppression will improve.
High salt conditions are frequently used for NMR of nucleic acids, you'll probably find more information in the papers on NMR studies of DNA/RNA.