I swapped a 303 tailcone onto a 315 transmission and you can indeed do this job successfully.

In my case, the 303 tailcone didn't completely cover that void where the lubrication tube for the speedo gear resides in the 315 body. I pinched-off and pushed in the tube and used JB weld to fill where the installed tailcone left that void.

But in your photos, you have a version of the 303 body that has the void but not the lube tube. Stretch's tear-down photos of his 303 also looked this way.

Therefore, your tailcone should fit without any modification, other than swapping the "spider". I swapped the entire parking cog with the attached spider rather than remove the speedo gear and install the spider.

After I had the car back on the road, I had an intermittent problem where the gear selector would not go into reverse or park without first turning-off the engine. This problem lasted for a few weeks and then went completely away. The transmission had sat for 6 years without use.

Of course, this is the opposite of your problem, but it may be related. The consensus was that the lockout mechanism that keeps you from shifting into reverse or park when the car is moving was malfunctioning. Probably a stuck valve related to the governor/secondary pump.

Now all is good.

__________________
1981 300TD 310k miles
1970 280sel 172k miles
1966 230 Fintail 162k miles

"Where are we going? And why am I in this hand basket?"