Well I'm not going to commit to the whole marine wire splicing expertise thing, but I will second warthog5's approach. Although me personally I not to big on those crip type connectors - personally I'd soldier then use a solvent to remove the flux, then the shrink tubing with glue, then liquid tape and then the rubber tape that welds itself together - hydro line men use it all the time.
Shrink tubing can be bought with glue on the inside of it or without. The glue type stuff really does add a weather resistance. The glue type shrink tubing itself is also much heavier then it's counter part - generally rubber.
The job is not a big deal to do yourself; just repair one wire at a time, then test continuity with an OHM meter to make sure the current passes through, then shrink wrap and seal. The only other comment I would pass along to you would be to mark any wire color changes you make along the way if you have any wiring diagrams.