i looked at the specs of that signal conditioner and it doesn't say about millivolts per volt 3mv/v like what the load cell puts out
"mv/v" is not a signal format, it's a hardware characteristic of the load cell. Feed it 10v, or whatever is within it's range, then take the 0-30mv full scale (or 0-[3 x excitation voltage]mv) and isolate/condition that with the signal conditioner to 0-10v or preferably 4-20ma.
Some thermocouple modules will even handle mv signals (such as from high current DC shunts, etc.) directly, but it's kind of hit and miss how well it works, so I'd stick with the signal conditioner. IIRC, you're doing this in a BRX, which at this time doesn't have any [local/native] thermocouple inputs anyway.