These controllers are basically PID's with a relay already built in. You can go for a larger relay but you are complicating things. You should have purchased them individually (PID and Relay) vs. the Ranco and adding another relay.
Check this website;
http://www.etcsupply.com/which-etc-model-need-a-6.htmllooks like 16 Amps for the 120V unit.
I run 4500W on the HLT and 1500W on the RIMS. I have a friend who uses 1500W to heat the HLT, but takes way too long. My 4500W leg is a 90Amp relay into 240V dryer/welder outlet in the garage. Built all my own PID/Relay/Thermocouple circuits. $25 PID's, $30 relay, $16 type K Thermocouple, + wiring and housing (old tool box).
FYI.