I take "best over a period of time" to be a better measure than going season by season and seeing who was better than him that year. That's an almost impossible standard. I hate to go back to Walter Payton again, but here's a guy universally hailed as one of the top 3 players of all time at his position by most. He won only one rushing title and led the league in rushing TDs once. And he wasn't always finishing behind HOF caliber players, either.
Skill wise, what sets him apart from most of the guys you named is his receiving ability. He's one of the best receiving backs ever, especially for guys that also got the bulk of their team's carries. For this reason, I'd say there would be a huge dropoff if you tried to replace him with Lewis for instance. Speaking of Lewis, and Alexander I also don't understand how it's a slight to LT that they did the things they did. By that logic, if a "pansy" like Alexander broke the TD record that should reflect negatively on every back before him, shouldn't it?
Your Martin argument doesn't make sense, either. You say his numbers are way better and note that LT has "awards and an MVP" but somehow their performances are indistinguishable. I can distinguish them pretty easily. The reason he won "awards and an MVP" is that in only 2 more games than Martin (170 to 168) LT's accounted for roughly 1,000 yds from scrimmage and 50 TDs more than Martin. And Martin is in the HOF. If by indistiguishable you mean neither played for a SB winner then ok, you got me.