With such a high boost ratio, my calculated duty cycle would be ~92%
which is near the maximum for most controller ICs
It's ~90% duty when operating in continuous conduction mode (CCM) but, if you lower the value of the inductor, you could operate in DCM (discontinuous conduction mode). If your controller permits DCM, it will be at a lower duty cycle. Here's a sample of what I mean from my basic website with a 33 μH inductor in CCM operating at 100 kHz and 90% duty: -
If you reduce the inductor to 22 μH you get an 80% duty cycle and DCM operation: -
The calculator is for ideal components so the percentage duty will be a tad higher. If you wanted to run at closer to 60% duty, you could choose an inductor of about 12 μH.
Is there a topology that uses a transformer to achieve such a high
Consider the above modifications first before taking the step to go to a flyback controller (more complex and requires careful selection of the MOSFET and/or leakage flyback snubbing).
If you decide that you need a CCM flyback circuit (1:4 step-up transformer) you can use this basic "ideal" calculator (also from my website): -