I might be wrong about this (Ford engine/chassis repair not being my strong point), but I think Manitou is just showing a relay, not the actual starter.
I *think* the starter is under the van a bit aft of the front axle. And maybe something there for you to check based on what I found.
I tend to lie around underneath the rig from time to time (in this case I think I was planning out my new/larger wire run from start to house batteries). While down there, I look around to see if anything looks amiss. In winter of 2014/2015 I was looking around and saw this delightful little number...
This is factory Ford wiring, and you can see the huge split in the negative cable with a nice bunch of green wiring inside it. I figured out that these were essentially the Ford start battery cables (the corresponding positive looked fine). My first thought was to just get new battery cables, but then when looking into it I found out that it's no longer "just" cables, but is instead a complete "harness" and would be rather involved to remove/replace. Also the rest of it looked fine.
Anyway, the reason I'm mentioning it here is that I think the "thing" with the two gold canisters (one small, one large) that these two wires go to is the starter. If you follow down roughly where the passenger side exhaust runs, you'll see it sort of just aft of the front wheels. To the passenger side of center (as I remember it - it's raining now so I'm not going out to check).
I didn't have any starting problems ever, and I can't tell how much this affected things because as a part of the whole project (new wire from start to house battery, removing recalled Surepower 1315, etc.), I also replaced the start battery. After this ugly negative wire was fixed, and the new start battery was in, it DID turn over and start really really fast, but I can't be sure what caused the difference. And before that I wouldn't say I ever thought there was a problem -- just that after it started like "crazy fast."
But maybe something to look at? A problem like this with your wire could cause a starting issue even if the battery was good.
For some reason I don't have any photos of the "after," but what I did was splice on a new section of marine grade wire, and then put on a new lug. I also improved that nasty bend that caused the split (or contributed to it). As I remember it I pre-bent the lug slightly to effect that. Then I put heat shrink over the connections. I have a big crimper and used FTZ lugs and dual wall heat shrink, so I felt it was better than new, even spliced. If I remember correctly it was 4AWG wire, but I don't remember the stud size for the ring terminal (easy to check thought if removing the old one).
Getting under there with the giant crimper handle "wings," plus holding all the parts and pieces in place while making the crimps was fun (not!). Good times
In the next post are a few more shots that sort of shows where this was (sort of...).