Is a "Spectral Tilt Filter" the best way to get an arbitrary slope and cutoff LPF?
yeah, that's the way we've been doing pink noise filters (or "pinking filters") since the 80s.

if you ignore edge effects it's made by alternating these pole functions:

$$ \log|H_{2k}(j\omega)| = -\tfrac12 \log\left( 1 + (\tfrac{\omega}{p_k})^2 \right)  $$

and these zero functions:

$$ \log|H_{2k+1}(j\omega)| = \tfrac12 \log\left( 1 + (\tfrac{\omega}{q_k})^2 \right)  $$

and the total frequency response is

$$ \log|H(j\omega)| = \sum_n \log|H_{n}(j\omega)| $$

(this is not done yet)