Slip yoke is standard issue and is a good thing, you can use transfer case from any F-Series truck regardless of wheelbase, if it was a fixed yoke then you'd be looking at Broncos only as donors. Not that you should be looking for one, I think you already found the problem:
The E4OD is a very long transmission, it puts the transfer case way back, but shifter has to stay in the same place cause of the cab floor. So Ford used a longer link on the E4OD as compared to the ZF5, if the correct ZF5 link is not available shortening the E4OD link is perfectly acceptable. As long as it's the right length that is, which yours sounds like it's not - what you're describing as behavior and the positions of the shifter in the pics suggests to me that someone cut the link too short, and you're hitting the detents in the transfer case before the shifter hits its gates right. The easiest solution would be to make yourself a new link, all it is is a piece of flat stock with two holes in it, don't have to be fancy. How long is your current link between the centers of the bushings holes, I can compare it to several links I got laying around and see if I can ID which one of them goes with my transfer case and then give you the correct length.
About the shift lever on the side of the transfer case, are you sure you're getting that much in-out play? All I can get out of mine is about 1/16", don't think it's even possible to have it slide in and out 1/2" without dropping out of its channels in the shift forks on the inside of the case... Check again how much in-out play you have with the welded link removed, I bet you'll find it's only 1/8" or less, which is probably nothing to freak out about.