I know this is an old question and maybe most of you have already found some good solution, including 10 Kg 1500 Watts transformers, any case I'll share my experience and the solution I've used to run it on 220v.
My experience:
A cheap chinese, rated 4000 Watts speed controller works fine and seems reliable (at least for me and the toaster, 1300W is less than half of the regulator limits and manufacturer optimism)
These also include a 10A fuse that will cut power if something goes as Murphy's law predicts.
The regulator introduces conmutation noise (hum), but it's not high, and for me it's even an advantage, if you're close, you can hear it humming, so if it does not stop on expectad time you'll be advised.
The only caution to have is adjust regulator to deliver 110 real volts (RMS) not the voltage shown by a typical multimeter, you can check explanation below, but I advance, 75 volts measured with a common multimeter match 110 volt real energy. (RMS)
I checked delivered voltage many times along many weeks ant it seems to be quite stable, always between 74-76 volts)
Other option if not having a multimeter on hand, may be the suggested test from zero to reasonable toast.
I also checked it, void and on duty.
Without a bread slice, the toaster will cut power in 10 seconds average (first time a little more until it heats up.
try to not go below 10 seconds, you''l be throwing more power than toaster expects.
Once toasting a real piece of bread, it requires around 1 min 52 secs to toast at medium grade.
I tested it up to 160 volts RMS (120 measured) and it runs faster but didn't appreciated anything more than heating wire brighter ant toast time shorter, no damage appears to happen, but I do not reccomend such experiments, start on zero and go in little increments to 10 seconds, then test bread.
I've been using it for a while and it seems very reliable
Once adjusted fix the regulator knob so it doesn't move by accident, once fixed check time again and correct if required.
(I used a bulky rubber washer that do not allow to turn the knob, anything tha fixes it)
More on the toaster,
As it is a simple resistive load, there is no too much danger if you apply a bit less or more voltage while adjusting, I tested it up to 120 measured volts (160 real) and below 50V, only change is heat produced and so, the time required to toast. Nichrom wire seems heavy duty enough to bear higher voltage pretty well for such little time, although they're not the designed tension, and may be not fine to conmutator wear, but my toaster didn't exploded.
P.S
I find the following explanation the most close to a toaster and is well explained, it's in Spanish, but you'll understand almost everything or may use subtitles.
For first explanation search on YT videos:
Valor RMS sobre carga con triac 2021
it's a 30 min video from "Hugo Grazzini"
For the second, concerning RMS search
True RMS (TRMS) vs Averaging Multimeters
it's a 7 min short video from " MultiMeter Channel"
A grounded 16A new power cable is a must, a simple and cheap improvement for your safety
A final note, if something smells og goes bad unplug the toaster, there's no other way to switch it off
I hope some find this info useful to convert their magnificent toaster, I love the intelligence on it.
This info is provided as my mileage, security must prevail so don't touch anything if you don't know what you're doing.
220 volts shocks could be fatal on first event and never are fun.
(Sorry for being anonimous, I was unable to log in...)
Ricardoch