yes i believe i have looked at that same schematic before, it all looks very familiar.
You need a steel toroid core for the main transformer, you can buy then from alphacoredirect for 3.50$ a pound plus shipping.. however the best deal on the internet right now is probably this one:
http://www.ebay.com/itm/281542186688 53 pounds of transformer for 110$ (from my point of view, shipping may be different for you)
as far as how big a core you need, a toroidal core with a core cross section equal to the EI transformer in those inverters will be significantly heavier and also more efficient by nearly an order of magnitude. (provided you use large enough wire) and the toroidal core will only consume about 1 watt per kilogram at 1.7T flux density at 60hz. however, the dc current that those inverters produce will certainly produce a lot more core losses in the toroidal transformer and you may not see any gains at all, except for the lower dc resistance of the windings
as far as saturation goes, you can sit and just listen to the inverter. you will periodically hear it buzz a little differently.
there are some differences between the transformers for the various models. some have a separate winding that is used for both buck and boost, others have separate windings, or a tapped winding. i don't think the exact turns ratio matters that much, when you get into winding large transformers often you can't match an exact integer ratio.
for an inductor, the yellow/white iron powder toroids that you can get out of most computer smps are worthless. you can actually increase the idle current of those inverters by adding them to the circuit.
i can help you with the inductor selection but it will be mostly guess work if you don't have a current probe for an oscope.
if you can find three ferrite cores from TV or computer monitor flyback transformers, or similarly sized cores, that will be sufficient for the inductor. how many turns also depends on the voltage, is yours 24 or 48.