Eating less moving more

Your general idea is correct.

I suspect your numbers may be slightly incorrect.

Only thing to do is to try. And evaluate your progress based on your weight trend over sufficient time.

You may want to consider the following questions:

What do you mean by losing weight? People often have an unrealistic expectation as to how fast weight loss will show on the scales and tend to misinterpret water weight changes for fat level changes. A lot of things influence accurate weigh-ins and the ablility to perceive accurately one's weight trend.

Have you optimized your way of eating? Different food choices may leave you more or less satiated. This may include both the variety, type,and timing of food.

How sure are you about the size of your deficit? Ravenously hungry is not usually associated with the beginning of an ~300 Cal restriction. It is more commonly associated with a much larger restriction.

Re read.

How are you evaluating you success or failure to lose weight.

You said you only lose weight while eating 1300 which leaves you so hungry you can't think.

This leads me to believe that it is at least possible that you're expecting continuous positive feedback from your scale as opposed to considering your weight trend over a period of 4 to 6 weeks when you're evaluating how much you're losing.

A 250 to 500 Cal restriction means that water weight fluctuations can easily obscure your underlying weight trend and you may have a hard time seeing your success unless you consider your trend over a sufficient time span.

If in your attempt to SEE progress you're (inadvertently) creating a larger deficit then you end up hungrier. and then that may explain why your hunger levels are more intense than what one expects from a 300 Cal cut.