The only way to make this work is if you eliminate one scenario from the possible outcomes you are betting. In this case it would be to remove the Dog-Dog parlay since you seem confident that at least one of the Favs wins. Working off of d3's 3.63 return on parlay:
$110 teaser to win $100.
$45 ML parlay BAL-SF to win $163.35
$45 ML parlay CLE-NYG to win $163.35
If NYG-BAL win you profit $10
If NYG-CLE or BAL-SF win you profit $8.35
If CLE-SF win you lose $200
Adjust your unit size as you see fit.