I have two 7B53As and one 7B92 sweep plugins.
In a 7704A, they all have similar problems.
There's no pretrigger leadtime, can't see the leading
edge of the waveform.
The trace unblanks about 4 nS after the edge. The sweep isn't even
monotonic in that first 150nS. The sweep actually reverses
in 16nS intervals creating a bright spot and severe distortion
if you move an edge through the region.
I've just checked out my 7704A using a 7B92A - and it works just fine. None
of the effects that you describe.
Craig