Need a step up transformer to power some 277 volt AC ballasts.

Can I use this advance ballast, but using the 120v as the input and 277v side as the load? For 35 to 50 watts max.

Similarly, can I use this transformer to get 347volts by using 120VAC input on the secondary tap?

What you need to take care is the apparent power, the real power is not that important.
But for a 50W ballast to exceed the 190VA rating would mean power factor of less than 0.25, I doubt anything of such power will have it so low, so it should be OK.
And for the 347V the limit is 20VA, so I don't know what you want to use it for, if that would be enough.

And count on a bit lower output voltage: Normally the transformers have parasitic drop, which is taken into account when designing it for the given rating. So a "277/120V" transformer will be wound more like "263/126V" (assume it is designed for 90% efficiency), so when reversing and loading the secondary could be just 250V when loaded.
Si9milarly the 347V one would have the output in your configuration about 280V (assume this would be designed for 80% efficiency, as typical for ratings in the 20VA ballpark)
You may try to measure the voltage without any load, calculate the conversion ratio from that, and then the winding resistances and calculate the voltage drop based on the load current.

So I could make use of the 277-to-120v working in reverse for about a 35w load. But to power 150 watts with the 347-to-120v in reverse will probably not work. I should use a real step-up 120-to-347v transfomer. Thanks for this info!