That action can be used only to take the Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action.

The Monster Manual (p. 9) says:

ACTIONS

When a monster takes its action, it can choose from the options in the Actions section of its stat block or use one of the actions available to all creatures, such as the Dash or Hide action, as described in the Player's Handbook.

Multiattack is its own action (i.e. it is not Attack, Dash, Disengage, Hide, or Use an Object). Neither is Eye Rays one of these actions. As such, neither can be used with the additional action provided by haste.

Both the beholder and the Benin (and any other monster) can only use the actions specified in the Haste spell. For every monster, the actions listed in their stat block are not those actions: they are their own actions. For the record, using a magic item is also its own action, so the beholder cannot use the basted action to activate a wand for example.

If a monster or PC wants to do something offensive with the Hasted action they must take the Attack action (one weapon attack only)- that means the specific thing they use must be a weapon attack, i.e. must have the words "weapon attack" in them.

Read strictly, you cannot make an unarmed attack or a shove or a grapple, however, I personally think that goes beyond the intent.

Excellent Idea! (MAYBE there's a loophole)

First of all, I'm impressed by this strategy! It's a great idea, and turns the tables on the Beholder extremely well. You might have some trouble targeting the Beholder from within the cloud yourself, but characters normally know where other creatures are during combat (the fact that the Beholder hovers may complicate this, but probably not unless the Beholder takes the Hide action).

There is a small potential loophole I noticed, but it's not ironclad (more open to interpretation).

Legendary Action & Lair Actions

The Beholder can use its eye rays with its Action during its turn, but must choose targets it can see. However, it can also use its eye rays in two other ways: one is with a Legendary action at the end of another creature's turn. This legendary action is described as follows:

Eye Ray. The beholder uses one random eye ray.

It can also use lair actions, one of which is the following (MM, p. 27, bold added):

Walls within 120 feet of the beholder sprout grasping appendages until initiative count 20 on the round after next. Each creature of the beholder's choice that starts its turn within 10 feet of such a wall must succeed on a DC 15 Dexterity saving throw or be grappled.

Note that neither of these descriptions requires the Beholder to see its chosen targets.

It's likely that the definition of the eye rays given in the Actions section of its description is meant to apply to the other (Legendary) rays as well. But this is ambiguously worded, and open to interpretation. Clearly, some parts of the description of the eye rays must apply (or else there would be no limit to the range of these Eye Rays, for example): exactly how much applies, though, is ultimately up to the DM.

Even if its lair and Legendary actions do not require sight, note that your strategy would pretty much halve the amount of opportunities that the Beholder has to target creatures directly (as opposed to lifting a heavy object above a character while they are in the Antimagic Cone, and dropping it). This makes this strategy an excellent idea in any case.