I don't like the handling of 4-4-4-1 hands entirely. I doubt they did (let alone most of us) either.
Define a sequence 2♣-P-2D-P-2NT as "both minors," but precisely "4+ in each minor and unbalanced." This allows 2NT to show 4-1-4-4 or 1-4-4-4 (the trouble patterns).
Responder can bid 3M as described by Bennet-Wirgren (natural), or 3D just asking for the minor. However...
Responder can also bid 3♣ as "Mini-Puppet Stayman." The responses by Opener:
1. 3M shows four cards (3♥ = 1-4-4-4 or 0-4-5-4 or 0-4-4-5; 3♠ same thing, but short hearts)
2. 3NT denies a three-card or longer major; Opener can instead "flag" his short major (4♣=♥, 4D=♠) if too strong for 3NT; 4♥ maybe 1-1 majors?
3. 3D shows an undisclosed three-card major (and stiff in the other major); 3♥ asks; 3♠ shows three spades, 3NT shows three hearts, and 4♣ shows three hearts but too strong for 3NT.
This seems better to me. The 3NT calls that showed these hands now are different, whatever you want them to be.