727 shifting into Park question

It's all good.
A coupla concerns.
You mention shifter goes forward till hits console, that's not right.
Were it me, with the car safe, chocked, etc, I'd pop that rod off the shift lever from the trans, and move that lever as far back as it'll go, that should engages the Park pawl, locking driveshaft.
Then go up and mess with the shifter, find out why it moves enuff to hit console when fully forward, as you suspected console may be out of place from previous owner.
It's possible to lift console enuff to work under, but with screws removed taking the console off just needs a small Allen key to loosen knob set-screw.
Count number of turns to remove knob, unscrew, remove knob , console should lift off, may be a wire for light.
Then you have clear access to shifter, - screw knob back on the number of turns you counted, then see why shifter doesn't engage Park gate.
With console off, it may work just fine, clean and lube moving parts.
You may find restricted movement cuz the knob needs to be screwed further on, or off, to get full motion.
Once you get full shifter motion, engaging the Park gate so shifter locks in P, leave shifter in P and go adjust the trans linkage with the lever still full back, so the adjuster pin fits directly into the lever hole, secure with clip/cotter pin.
Install console as nec to provide the motion needed.

Good luck