[5e Question]

I am building a blade pact warlock that uses a Glaive. I intend for her to have War Caster and Polearm Master Feats.

My DM has some (legitimate) balance concerns about attacks of opportunity with this combination and I'm hoping for some clarification on it (not just opinions.)

Booming Blade - As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range, otherwise the spell fails.

War Caster - When a hostile creature's movement provokes an opportunity attack from you, you can use your reaction to cast a spell at the creature, rather than making an opportunity attack.

Polearm Master - While you are wielding a glaive, halberd, pike, or quarterstaff, other creatures provoke an opportunity attack from you when they enter your reach.

With the above combination, I could do the following:

1.) Make an Opportunity Attack with my glaive due to Polearm Master (Rick Deckard confirmed that Polearm Master and War Caster don't stack.)

2.) Cast Booming Blade on enemies that leave my 10ft reach due to War Caster.

3.) Cast Eldritch Blast on enemies that leave my 5ft reach due to War Caster.

My DM is concerned about the number of Opportunity Attacks this combination would generate and isn't sure that a person could threaten with their reach weapon and then take their hand off their two-hander to then threaten in melee. The Errata clarified that two hands need to only be on the weapon if you're attacking and that you can lift your hand off to cast a somatic spell. I don't think it's that farfetched so assume you could also take your hand off to make an opportunity attack using War Caster.

Has anyone else seen this come up?