Self levelling isn't really designed to be a finished surface, it is designed to have tiles or flooring laid on top. Also you'll lose half of it down the gaps at the side. Unlike other cement based products it goes from hard to set pretty quickly.
You have the desired finish height you'd be better off screening it. Mix up a 1 part cement to 3 parts sharp sand, you want the mix to be dry. The best way to do it is to put the sand and cement in a flexitub and thoroughly mix it together with a bucket trowel (the set I've linked to here doesn't have a bucket trowel but you can use the guageing trowel for the same purpose plus it has everything you need and costs less than one decent bucket trowel) once it is well mixed together you need to add a little bit of water at a time until you reach the desired consistency. You want to be able to pick up a handful and form it into a ball in your hand with light pressure and not have any liquid showing on the surface of the ball, if you go over just add a little bit more sand and cement.
Put the mix on the hearth and roughly smooth it out with the trowel. When you're nearly there get the float (plastering trowel) and holding that at a very slight angle drag the surface level adding a bit more mix if needed.
Once it is at the right level leave it for 5 -10 minutes and polish with the float, using the whole flat back of it to apply moderate pressure and really smooth everything out and bring up a nice finish.
Do you mean using PVA as a bonding agent? If that is the case then SBR is a better option however in this instance given the area is so small then partially bonded should be ok.
I've laid a fair few screeds in both domestic and commercial environments and never heard of mixing a screed with PVA.
Self levelling isn't really designed to be a finished surface, it is designed to have tiles or flooring laid on top. Also you'll lose half of it down the gaps at the side. Unlike other cement based products it goes from hard to set pretty quickly.
You have the desired finish height you'd be better off screening it. Mix up a 1 part cement to 3 parts sharp sand, you want the mix to be dry. The best way to do it is to put the sand and cement in a flexitub and thoroughly mix it together with a bucket trowel (the set I've linked to here doesn't have a bucket trowel but you can use the guageing trowel for the same purpose plus it has everything you need and costs less than one decent bucket trowel) once it is well mixed together you need to add a little bit of water at a time until you reach the desired consistency. You want to be able to pick up a handful and form it into a ball in your hand with light pressure and not have any liquid showing on the surface of the ball, if you go over just add a little bit more sand and cement.
Put the mix on the hearth and roughly smooth it out with the trowel. When you're nearly there get the float (plastering trowel) and holding that at a very slight angle drag the surface level adding a bit more mix if needed.
Once it is at the right level leave it for 5 -10 minutes and polish with the float, using the whole flat back of it to apply moderate pressure and really smooth everything out and bring up a nice finish.