Can the Shield Master feat's bonus-action shove be used to make an improvised weapon attack?

Question

Do the rules allow the bonus action shove (special melee attack) from Shield Master to be "converted" to a regular attack for use as an improvised weapon attack?

Since a shove is a special melee attack that replaces a regular attack (at the choice of the player) when you make an Attack action, could one "convert" a bonus-action shove provided by the Shield Master feat into a regular attack using the shield as an improvised weapon?

This would create value for people discouraged by the recent rules clarification regarding the timing of this feat. The value added would be that a class with Extra Attack could take the Attack action, use their first attack to shove, then attack with the rest of their attacks. Having taken the Attack action, you then generate a bonus-action shove, which ideally could also be converted back to an attack using the shield as an improvised weapon.

(I like the flavor of a shield master using his shield for an attack.)

Answer 1

No, you can't use the bonus-action shove to attack in any other way.

As you noted: Per Jeremy Crawford's clarification on Twitter and subsequent 2019 update to the Sage Advice Compendium, the bonus-action shove from Shield Master can only be done after completing the entire Attack action.

The first bullet of the Shield Master feat (PHB, p. 170) says:

If you take the Attack action on your turn, you can use a bonus action to try to shove a creature within 5 feet of you with your shield.

The word "shove" refers to a specific thing in 5e, described here in the rules:

Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.

The target must be no more than one size larger than you and must be within your reach. Instead of making an attack roll, you make a Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). You succeed automatically if the target is incapacitated. If you succeed, you either knock the target prone or push it 5 feet away from you.

The feat makes an exception regarding the timing of your shove, but everything else about it is the same. The mechanics for that shove are collectively described in the feat and in this section of the rules.

The rules on improvised weapons describe the mechanics of attacking with something that is not a weapon or otherwise designed to attack with. They don't describe the timing of such attacks.

The Attack action lets you make an attack (or, with the Extra Attack class feature, multiple attacks) using your action. The rules don't specify what you have to make this attack with, so you can make these attacks with any combination of weapons (normal or improvised) or unarmed strikes.

No rule allows you to substitute that regular bonus-action shove (granted by Shield Master) for any other sort of attack or action - including the use of your shield as an improvised weapon to attack (and do damage). In the absence of such a rule, you can't do so by RAW.

(As always, your DM could house-rule otherwise, but this would essentially be granting you a free attack every turn.)

Answer 2

No

A regular attack can be converted to a Shove but a Shove can't be converted to a regular attack.