A couple things keep coming up in the comments, so I figured I would address them here:
In getting ready for this, I was able to find the pats diagram for the pump, it shows a one-piece, rigid coupler attached to the shaft.  In fact, the shaft and coupler are listed as one part number.  It’s not a lovejoy or other sort of flexible coupler.  And yes, the fit on the spline as shown is probably a little tighter than it should be, but after several rounds of assembly and disassembly, the fit did loosen up a bit.  I’m assuming there are some small burrs in there that got knocked down.  If I had to do it over again, I probably would make take another .001 off. Additionally, the hex shaft is about .003” under the nominal dimension, and I made the broach to the nominal dimension, so there’s some wiggle on the connection on the hex end, so I’m not particularly worried about misalignment or vibration issues.  Also, a flexible coupler probably wouldn’t have fit in the pump housing.

The other two things that come up are 1) why not modify the shafts, and 2) why buy something to make it work.  The answer is: because Jeremy Makes Things. I wanted to see if I could do this, and do it as close to the right way as possible. I knew the theory behind doing an internal spline, but theory and practice are two different things. I wanted to push my skills.  As happy as I am with the end result, this project was just as much about going through the process.

Fellow machinist here, proudly making what nobody will ever see

I just love when somebody else volunteers your services

Nice to see a machinist who is more about the work and less about the image and vanity. Great to see real old school tools being loved and worked. Subscribed on first go.

I love your "toolception". Making a tool, to make a tool, to make a part to fix a machine.

You know you’re watching a real master when they casualy stop the project to forge or machine a custom tool they need. 🛠 Custom internal splines are no joke, but your precision makes it look seamless. This is exactly what DIY engineering and custom toolmaking is all about!

Remember, "Persistence is the bitter part of valor."

I'm not a machinist but I thoroughly enjoyed watching the process of making that adapter

We had a spline shaft come in pieces, to the shop. I made a series of kerfs, carbonized it, and heat treated. Made a short broach to clean up the spline. Used a dividing head for the shaft. I think you should always knurl, as slow as it goes. Too often, the knurling wheels, weld on to the pins. Can't keep enough oil on them, knurling can produce a lot of heat.

Think the world forgot about good tool die maker. Everything that works mechanically has a good tool maker behind it. Thanks

I love the fact that your knuckles are positively devastated with cuts and Knicks lol, that's evidence to me that you've been fighting with this for a while!

You know you achieved complete machining self-reliance when “That’s probably not the last one of those I’m making” Is followed by making a goddamn broach. And to prove it, just make another one! Awesome job!

Jeremy,  Thank you for sharing your (mostly) entire thought process plus the "oopses" that you ran into instead of doing like most channels that "hide" their mistakes and other things that don't go correctly.  Seeing how another home shop Machinist goes about a job with similar (actually better! ;) equipment and raw materials is very helpful as well as giving an idea of that "aw sh**s" to expect is worth its weight in YouTube gold!

I was really impressed not just by your skills, but your camera work, narration & the inclusion of issues in this difficult project. I believe this demonstrates your high intelligence & educational ability. Any student would be lucky to have you as an instructor. 👍

16:11 buddy's got his machining bible in the shop

Your skill at machining is amazing. You put all of the effort in your projects and they surely pay off! I still can't believe you just have 8k subscribers

The old saying " no good deed goes unpunished " rings a bell by the looks of your knuckles lol. Excellent work and tool making skills.

Thank you!  As an old fellow who's been around and seen a few things . . . I learned a few things and was entertained in the process!  Thanks again.  You have a new subscriber.

I dread to think of the number of hours you put into this, but the results are very pleasing!  I think a machinists jack might have been useful under the end of the workpiece on the shaper, it did seem to be deflecting a little.

Years ago I had to cut an internal spline for a hydraulic motor on an adapter much like this video. Instead of a shaper I did it on a Bridgeport mill using the quill as the ram with the part on a rotary table. My boss couldn't believe I pulled that one off.
Fun times.