I'm a HAP landlord. Like you some of my tenant's were moved from the council paying them, and them paying me to the HAP. Where the payment is directly to the landlord. And the tenant pays the council a contribution. I think the tenant can pay it directly at the post office where they get their social welfare or they can pay a direct debit.
It was a nightmare at the beginning to set it up paper wise. They were terrible to deal with. But I had another tenant join HAP this month, previously not a social welfare tenant and it was a breeze as I already exist in the HAP system and I knew exactly what they needed.
HAP payments are paid from a Limerick office, separate to the councils. Into my bank account.
That is not the main problem, it's the fact they pay one month in arrears. Easily solved by you paying that to your landlord and agreeing now to do so. (with my tenants we just got them to pay extra over a period of time as it's hard for some to get a month's rent all of a sudden.
As regards inspections and standards. There have been zero HAP inspections and zero inspections ever by two city councils in my more than two decades of being a landlord.
Last year one tenant didn't pay the council, after a few weeks the council sent me a pink letter about this, it all got sorted (tenant paid up) but I figured out that a landlord could be a long time out of pocket if the council don't notify the landlords immediately.
One advantage for me as an non resident landlord the HAP deducts 20% tax and that means I've already paid the taxman when I do my tax returns.