We all see many anecdotal stories/testaments about SRW trucks and ability to tow "just fine for years" "no problem". Etc. Payload capacity for the actual truck is one necessary number. Mfg specs show higher than actual truck due to options and cab style. I know of more than one who ordered the SRW truck because the spec sheet said payload capacity was over 4000 lbs, in one case it was 5000 lbs... The new truck was ordered and delivered with a tag that said 3500 lbs., which is more normal. Your Big Horn fully loaded is the other weight you need to know. Not a percentage of total, but actual. My fully loaded 3055RL is 3400 lbs pin weight. We're full time, so may be heavy, but you only know with actual scaled weight. My guess is you need the DRW, but only by using actual numbers can you be sure.
PS, also payload includes passengers, hitch weight, toolbox, auxiliary fuel tank, etc