Ian, I have the same 90 amp HF welder, except mine is the older blue model, and my welds looked just as bad as the ones you do lol.
(Just look at my old forge welding vids on my Youtube channel for proof!)
It's been a while since I've had to use it, but one thing (along with preheating) I do to keep a handle on the billet is to leave one of the layers in the original stack longer than the rest, usually a layer of the thicker 1084 near the middle of the billet. I grind a chamfer on the end of the handle as well as the end of the single 1084 layer that is sticking of of the back of the billet. Then do your preheating on the end of the 1084 before welding them together. I choose the 1084 as it's thicker and doesn't have any nickel, which is just one more chance to possibly complicate things, at least for me.
When you cut to re-stack the billet, keep that bit of extra material extending our from the end so you can get a fresh weld on the handle for you next forge weld and drawing out, then repeat till desired layer count is achieved.
I'm by no means an expert welder (or even a decent one), but I noticed that with these cheaply made lower amp welders from HF I need to use everything I can to my advantage for a successful weld when welding handle to a billet that;s gonna take a lot of heating and beating. I've never been able to get a handle to stay/weld on the flat end of a thick billet (like yours), so just keep a layer or two extended from the back so that welder is able to easily penetrate its thickness and remain attached till I'm finished drawing it out.
One more thing that may also help (I could be wrong though) is to give the welded section a stress relieving cycle by heating is with a touch to a dull red and letting it air cool before you begin hammering on the billet.
Anyway, I hope you're able to get it to work for ya
~Paul
My Youtube Channel
... (It's been a few years since my last upload)