Thanks for your answer.
I did try (1) quite extensively, with something like 20,000 draws, up to the point where I sample even extremely unlikely values of t. There wasn’t the slightest change.
Regarding (2), that’s a good suggestion. I wasn’t familiar with Google Colab. But the result is the same. Here are the plots I get with pymc4 (v4.1.4)
and for the other model
So you think I should try to install pymc5 now? 
By the way, I should add also what happens when I use 100 data points (still always 1) instead of 10: the non-marginalised result doesn’t really move and the difference is even more pronounced.
Non marginalised:
Marginalised:
