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For many years I've used Penguin 300/330 power filters fitted with Hydro-Sponge prefilters, and this has worked very well for me. I just bought a new Penguin 350, and find that the intake is now rectangular instead of round, which means I can no longer easily attach a prefilter to it. Can anyone suggest any workarounds?

I am often away from my fish room for weeks at a time, when my family does the minimum necessary to keep things going, so solutions need to be robust enough to not require frequent maintenance. IMO, a media bag covering the intake strainer is unlikely to provide a sufficiently robust solution.

Simply placing a media bag around the rectangular intake is not going be satisfactory as you have already concluded.
However, one of the best pre-filters I have used might work to your satisfaction.
The first thing you need to do is replace the new intake with a more conventional cylindrical type.
You may have to visit the plumbing department of a large hardware store and buy tapered barbed fittings, some flexible clear or black tubing and make an adapter which will accept an AquaClear type of intake or something similar.
Once you have that project completed either go back to a sponge pre-filter or my preferred method, fill a media bag with the springy, coarse filter material sold by Eheim as Efifix. This material will keep a media bag expanded and may be slipped over the end of the redesigned inlet and held in place by a heavy duty rubber band.
This allows you to spread the suction over a very broad area and they are not as prone to clogging as sponge pre-filters and are very easily cleaned and reused. I have to clean this type of pre-filter 3 or 4 times a year and not even baby Cherry Shrimp let alone fish fry are able to go through nor is the suction so great the smallest of animals can escape. Shrimp spend a lot of time cleaning the bits of debris that collect on the surface of the expanded media bag and the filters need cleaning less frequently.

Thanks, Larry. Filling a media bag with Ehfifix and using that as a prefilter is an interesting idea. I'll give it a try. But this would seem to work regardless of whether the intake tube is round or rectangular, so I'm not sure I understand the logic of the first part of your recommendation about redesigning the intake. What am I missing?

It would take a larger media bag and more Ehfifix but you could do the same thing. It's just that you are already beginning with a large intake so bundling it in the way I described would be more of an eye sore in a display tank. If it is stripped down grow out tank aesthetics
is less of an issue.