Lets say I came up with something like this:
https://www.ebay.ca/itm/221587713725

What kind of 120v or 240v output could one expect? Something less tha 800Va I presume?

It will depend on the power factor of the loads that you run.
But yep probably a bit under the 800VA.
The cheapest way I have seen to get a higher powered torroid is to buy a 240 to 110 commercial transformer. They are rated ridiculously but if you got two and stuck them together then you can increase the rating easily.
step down transformer

The one in the link says it is 5000 watts but is actually rated at 3000 watts.
That may be an ambitious rating too, but still a cheap transformer.
Then of course you would have to wind it to suit your needs
Pete

Sorry the link is the the wrong one, somehow it pasted your link in
5000 watt transformer

Pete

I had no idea those cheap (or at least cheap looking) stepup/stepdowns have
toroids. I figured some cheaper structure.New respect, so a used may yield something cost effective.

I bought one of the 240 to 110 converters to see how they were. Mine was supposed to be 3kw. The transformer in it is more likely rated to about 1kw, but still it was only about $100 or less Australian dollars.
I put a new low voltage winding on it and left the high voltage winding in place, I plan to build a small inverter with it.
It is still much cheaper than buying a new torroid for the job.
good luck
Pete

Welll, hmmmm…  slightly veering away form the original intent:

I never liked the victron auto transformer and was looking for a real Hammond/GE? WHOEVER  2:1 TRANSFORMER

Any reason I couldn’t parallel two or more of these toroids to achieve the required power handling?

Plenty of people here on the site have paralleled transformers to increase the rating.
Most parallel the high voltage windings of transformers they get from defunct Grid inverters.
Then they stack the cores vertically and wind a new low voltage winding around the cores that they have stacked.
To use two transformers in parallel without a common winding may not work well unless they are both identical in every way.
I have made 4 kw torroids by getting two 2kw torroids, unwinding them, gluing the cores together and fitting new windings.
It is really not that big a job. The larger the cores are the less windings they need.
Have a look around on the site, there is a lot of information about transformer design here.
There are online calculators that allow you to work out how many turns you need for any core size.
Pete