If you really need to solve this problem, then a company called
Salicru make votage regulators that work much better than the ferromagnetic types with difficult loads. It is esentially a transformer with a tap-changer, but the tap-changing is done through semiconductors, so unlike mechanical tap-changers it corrects cycle by cycle.
Because the company are not native English speakers (they're in Barcelona), theres some real howlers both in their documentation and their website, but the products do what they say on the box.
I dont know what their distribution in the USA is like, but here in little ole NZ we have a distributor, so they must have a source in the 'States. All they list for the USA is an email address, which is
america at salicru dot com
Another alternative is what is effectively a UPS without a battery; look to
Visicomm Industries for their range of static frequency converters; these converters will produce 50hz or 60hz out irrespective of the input frequency, and have a -15%/+20% input voltage toleration, whilst producting 1% reguation at the output. So it'll happily do 60Hz to 60Hz "conversion" whilst regulating the voltage well. These guys are local to the USA.
Note that neither of these options are low cost; if you need stable power of more than a few watts with a difficult load from a dodgy supply, there are no really cheap options. However, at least your customer will know his next few thousand dollars will deliver results not failures.
My final (and low cost) suggestion is for the owner to take the toaster oven to someone who is competent to rip its covers off and alter it; the elements won't care much about the voltage dips, but the electronics do, so dissect the internal wiring to put the electronics power supply onto a different inlet to the rest of the oven, and use a small standard double-conversion computer UPS to supply just the electronics. Of course, this will destroy any listing the device had...
