If all this passes the next step is to look for voltage drops in the electrical system. Backprobe the R/R connector, put red DMM lead on red R/R wire, put the black DMM lead on the positive post of the battery. Start the engine, read the meter -- the voltage you read is what is being lost between the R/R output and the battery terminal. This will be the sum of wire resistance, connections, the main power fuse and any associated connections. Now backprobe the black wire in the R/R connector with the red DMM lead and put the black DMM lead on the negative post of the battery. Start the engine, what you are reading is the voltage drop on the negative power lead. Ideally these drops should be <0.100 volts but real world you may see a bit more. When you do the voltage drop test, probe the actual battery post, not the connector. By probing the actual battery post you will also be reading the quality of the battery cable to the battery post.
Let us know what you find! If all this passes, you are probably going to need a current meter or amp probe capable of measuring 60 amps or so.