The 6.5 is slightly smaller, like Bob said, and when you fire it in 7mm bore it will either not engage the rifling or engage rifling only partially. Form the description of your experiment, it appears that the projectile mostly engaged the rifling.this is the 1st gun i've ever fired...i leave it to the experts lol but i'm just saying i had 3 different people look at it and call 6.5 without knowing anything. that being said i have no idea if they know what they are talking about. what happens if you put a 7 in a 6.5? will it just not fire or will it blow up in my face?
Overall, 7mm Mauser and 6.5 Swede were made for small ring mauser action, there should be no blow ups because the action is designed to handle the pressure generated by either of the cartridges.
The problem is the mechanical condition of the action. You have a Spanish military mauser in 6.5 Swede, Spaniards did not make their military rifles in 6.5 Swede. Do you see the problem?