If you have a signal generator, I would try moving the frequency around to see if the observed offset at fast sweeps changes across the span, or if it's a constant. If you don't have a generator, you could change the center frequency of the sweep, but it's not as good a test since it's potentially changing other variables.
This would at least help you understand if you have a sweep ramp gain, offset, start delay, or perhaps some kind of non-linearity issue at higher sweep rates.
Examining behavior at other largely different frequencies and other spans might provide some clues too.
And, as TSL said, all this assuming you've run a successful cal.
Also take a look at the center frequency accuracy spec. I still think it's odd that it does what you see, but if I'm interpreting this right you're still in spec being off by 1.5MHz @ 100MHz span:
Center frequency readout accuracy
Spans ? n x 5 MHz ± (2% of frequency span + frequency reference error x center frequency +10 Hz)
Spans > n x 5 MHz ± (2% of frequency span + n x 100 kHz + frequency reference error x center frequency)
where n is the harmonic mixing number, depending on center frequency:
n center frequency
1 100 Hz to 5.8 GHz
2 5.8 to 12.5 GHz
3 12.5 to 18.6 GHz
4 > 18.6 GHz
from:
http://literature.cdn.keysight.com/litweb/pdf/5091-3385E.pdfI don't have this analyzer, so I certainly yield to those with more direct knowledge of its expected behavior.