I have had 2 different trainers I set up to do flat spins. Moving the CG back, and getting as much rudder and elevator as possible were the key parts.

On the trainers, most of them have so much down-thrust that you can't spin them at full throttle, the engine pulls the nose down and out of the spin, so it has to be done at idle. Playing with the throttle a little in the spin can sometimes find a "sweet spot" where the nose comes up a bit more, but it's still not enough to pull the plane out.

Adding rudder area and reducing vertical stab area helps a lot as well. I did that to one trainer and the spins were quite impressive. It would take about 4 rotations to exit a fully developed spin if you just released the controls. A bit of opposite rudder and down elevator stopped the spin quickly.

Anyway, the point burried in there is that the engine thrust line can play a part in how a plane spins.