Of course if your only concern were the proportion of the free play you converted to cash (having no problem putting up additional funds to actuate this) then your best option is taking as large a dog as you can find at the book with the free play and betting the opposite side if and only if the fave/dog line set satisfies the following inequality:
F > 100 - 4/3 x D where dog odds, D ≥ +100 and fave odds, F < -100
If the inequality is not satisfied then you'd be better off using the 3-team parlay method.
To give a specfic example: let's say the book where you have your free play is offering a dog line on a particular game at +500. If you can lay off your risk at better than 100 - 4/3 x 500 ≈ -567 then that would be a better option than the 6:1 3-team parlay.
So this implies that with a dog line as high as +210, you'd still be better off taking the 3-team parlay than you would using your free play to scalp with a -181 fave.
With a +150 line at your free play book? You'd need to find a +100 on the other side to justify the free play scalp.
The moral? In general, don't scalp favorites or small (< +300) underdogs using a free play. You'd just be throwing away your money ...