If FCA credit declined you, any dealer will too (they’ll likely reuse that prior application). US Bank or Ally might approve it, you’d have to apply to see.
Number of trade lines is only one aspect, DTI is another, age of trade lines is another.
The difference between financing and leasing is who carries the liability: if you finance, it’s all you (even if someone lends you their money). If you lease, the leasing company has it and expects the car returned on time in the agreed time. Your prior history with one card is sufficient credit history to demonstrate someone can be trusted to borrow/use/return their collateral: they don’t want the risk based on what they see, which likely won’t change overnight.