It would have helped if you'd kept the camera over your dash lights for the entire crank but you got there eventually
Dash lights dimming: I'd say worn bushings, brushes or commutator - if you're really unlucky, all of the above.
If this is the case your ignition system will be ramming current into the starter to compensate and this will explain the 'burning plastic' smell - you're frying the harness.
Do the battery cables (positive and negative) get warm after the crank?
Personally, I'd rather you didn't try this again as you risk permanent damage to the wiring harness which is a significantly bigger problem than sourcing a new starter - which is what it sounds like.
Verdict: reasonably safe bet that it's the starter
