I'm adding my 2c not because I am an expert in this field, but because I made critical errors in this step of my conversion project. My transmission started leaking from the input shaft within a few blocks of the first test drive, and I drove the conversion less than 50 miles before scrapping the project due to lack of time, space, and money to redesign the adapter assembly.
put it on your input spline and spin the gearbox over, does it wobble? Put it on your motor and spin that over, how much does the welded bit wobble? Put a DTI on it and work out how far out it is. It will be out of alignment to some degree, how much determines how long the spline and/or coupling will last
Agreed, use the dial indicator when the coupler is attached to the motor. Looking at wobble with the coupler slid onto the trans input shaft may be misleading and difficult depending on the transmission design, as well as the aforementioned clutch disc spline-slop factor. Also as mentioned earlier, transmissions that use a pilot bearing can be a bit wobbly at the input shaft when detached from the accompanying engine.
Can you confirm if your crankshaft has a pilot bearing or not?
It appears your project may be moving faster than the advice can come in and be appreciated. The momentum of an exciting DIY build can be great, but can also corner you if something gets overlooked or compromised. You have been given some legitimate and free Mechanical Engineering advice in the above posts, so make sure you understand the concerns that have been raised. I ignored or glazed over some advice from experienced members here and got to see the results, even though myself and the machinist agreed on the feasibility of the adapter design.
Can you get the machinist to run the piece with a dial indicator, and show you how the parts were made centric for the welding? Did they put machine screws in the threads and torque them onto some properly sized rod for that portion? If you did not provide them with a runout spec or some measurable expectations then you probably cannot expect them to compensate you, but you may be able to save damage to your gearbox by stepping back and taking some time to confirm some things.