I put an H41 in a 4/73 FJ40 with the original F engine. The 4 speed trans (H41 or H42) from an FJ40 is 3 inches longer than your J30 3speed. I had both shafts modified accordingly. Sadly my slip splines are kind of worn on the rear, in hindsight I should have had the front shaft shortened to fit the rear, and put the rear parts on the front as they have to make a whole new tube for it anyways at the driveline shop. I also have a PTO winch, so I had to make a new shaft for it too.
As for the cover question this post started with, I think that cover will work better than the earlier 3speed covers. I kind of wonder if the actual early 4speed course output transmissions had a different top plate. The tub on my 4/73 accommodated the 4 speed just fine, the raised floor area by the fuel tank had extra room for the high/low shift linkage that was not needed for the 3speed. Also my cross bar on the frame is tilted back and has the bent loop with plenty of room for the e-brake. I think the drum will even still pull off. These are all interesting observations as there was an optional 4 speed by 73, so the frame and tub must have been compatible by 4/73.
For my conversion I did have to take some of the transmission shifter hole out, and I flipped the crescent shape over and put it on the other side of the hole, but now I can't remember if I had to move the hole forward or back. This helped fill the hole back in. Looking at my photos, you must need to move the hole forward. I used "U" nuts to hold the boots on as I recall. I also opened up the transfer shifter hole like the hump shown by the original poster.
I wanted to get a better seal and sound control on mine, so I used FJ60 boots. They are nice heavy boots, have the second inner liner and don't leak air/noise/water like the originals, especially the transfer case vinyl cover. They also have a big footprint and covered up all the hacking and paint touch up. Pro-tip, the 4 speed shifter cane is smaller diameter than the FJ60. The cover hole will be loose. I used something like this
Climax 1/2 in. Bore Zinc-Plated Mild Steel Set Screw Collar-C-050 - The Home Depot a collar that I had to file out the center a tad till it slipped down the cane to the right spot and then the boot fit on it. I welded a washer to the back side so the boot will not push off it, hidden by the boot. Set the set screw and you have a seal.
Below is my prior boot config, the PTO and trans were custom jobs, and what I have now. Ignore the flat part of the trans cover that extends rearward, it doesn't cover anything. That started life as a Hurst shifter cover we used, but the rubber cracked out, so I used the plate and sewed up a vinyl boot like the transfer. I don't have a pic of the holes though.