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UCC28910: Having trouble designing a supply with Webench tool

Part Number: UCC28910
Other Parts Discussed in Thread: UCC28911, , , UCC28911EVM-718, TIDA-00618, PMP

I'm trying to use the Webench tool to make a small UK mains to 5V isolated supply. I'll lead you through my though process, perhaps you will see where the problem is, or where I'm missing something. Maybe I'm being silly and it's all obvious.

Webench params are as follows: AC/DC 85 to 265VRMS 50Hz input, 5V 0.5A isolated output, design optimized for high efficiency, ambient set to 60deg.

Solution ideally is 70-80% efficiency at light load, as device would operate at about 100-200mA most of the time (running of a filtered 3.3V downstream converter), occasionally drawing up to 500mA to drive buzzers and LEDs (PWM at about 5-10kHz) from 5V supply. So the output voltage can be fairly noisy within some limit (+/-0.3V maybe).

The enclosure will be tight and will not have good convection, hence efficiency requirement, so we don't generate too much unnecessary heat. There is only about 10mm of vertical space for components, which severely limits transformer and capacitor size.

Looking at the options provided by the tool, I'd rather have an integrated switch, and use a design without opto feedback to reduce BOM count and footprint size. That leaves me with UCC28910 or UCC28911.

For my application, the difference between these these two ICs looks marginal, so I could go with either one. I'll take UCC28910 because there is stock at Mouser.

This is the point where it gets difficult for me. Webench generates the design, it looks fairly decent with 75-80% efficiency at 200mA, but BOM shows me I need a custom transformer:
Core=TDK, CoilFormer=TDK, Core=B65807P0000R049, CoilFormer=B65821C1008T001, Core Type = RM6 LP, Core Material = N49, Turns Ratio(Nps) = 59:4

For a quick 10x batch I would prefer off the shelf components. I switch to Customize Design and try to select the off the shelf transformer, but I don't see any options, except using a custom one. Hyperlink on the transformer leads to "Page not found". I tried changing alternate part selection limits, thinking maybe the limits are too tight so it doesn't find anything. Nope, nothing. It would be awesome if I was able to select an off the shelf transformer and recalculate design values with this tool. Is it possible at all?

The direct approach didn't work out, so another way would be to look for a reference design and see if it has a transformer I could use.
UCC28910FBEVM-526 reference schematic uses 750313739 transformer, which is a no go as it's 16mm high.
UCC28911EVM-718 schematic uses 750315369, which unfortunately is also 16mm high.
I went through the Wurth range, and 750312723 seems to fit the bill (10.41mm).

Can I somehow import 750312723 in Webench design to automatically recalculate values?