There is a difference in language registers, amoindrir is literary, almost never used in the conversation and rare in books, diminuer and réduire are less expected in a colloquial situation while baisser is not linked to any register.

I’m close to your guesses when comparing these verbs:

Baisser from bas (low, bottom) (lower)

Diminuer relates to diminution, mineur, mini. (smaller)

Réduire relates to réduction (smaller)

Amoindrir relates to moindre and moins. (lesser)

Usage is sometimes different, especially with baisser which is often used in phrases where the other ones can’t be :

Je baisse la tête¹, la voix, le ton, les yeux, les bras, la visière, le pont-levis…

Sometimes, the three first verbs are interchangeable:

Je baisse/diminue/réduit le prix/le débit/le niveau/les gaz/le volume: all are fine.

Réduire has some specific meanings (shared with the English "to reduce") like réduire une équation (mathematics) or réduire une fracture (surgery).

Amoindrir is rarely conjugated, many of the few occurrences use the infinitive:

Amoindrir le rôle
Amoindrir le pouvoir
Amoindrir le sentiment
Amoindrir le choc

¹_{Je diminue and even more je réduis la tête are possible, but with a huge difference in meaning 😉}

I quote (because I cannot comment), and looks at the meaning for a physical object (primary sense of each words):

Baisser from bas (low, bottom) (lower)

The object don’t changes its size, but goes to the bottom.
« Baisser le volume sonore » is not related to the acoustic pressure, but to the controller of the amplifier. It is in fact related to « baisser le niveau sonore », or « tourner le bouton du volume sonore vers la gauche » or even « baisser le curseur du volume sonore ».

Diminuer relates to diminution, mineur, mini. (smaller)

Change its height, not its width nor whole volume ; changing the height/width ratio.

Réduire relates to réduction (smaller)

Reduce its size, but in all directions. Height, and volume, without changing the height/width ratio.

Amoindrir relates to moindre and moins. (lesser)

Make its negative (or sometimes positive) effect less important.
« amoindrir le choc ». It will still be important, but mitigated.