Applying to a new position after a few months?
The solution to your predicament lies, as I see it, completely in how you approach your reference writers.

I would approach them from the point of view that a great opportunity has presented itself to you in a very untimely fashion given that, "I already asked you to write a reference for me a short time ago. I hate to ask you to do this yet again, and I'll completely understand if you decline." That sort of thing.

Hopefully you saved a copy of their prior recommendations so they can use them as an easy guide. Offer to help them if they are pressed for time.

A great opportunity should not be ignored simply because someone might have to do a little bit of work for someone they've believed in very recently.

This just happened to me recently. A friend asked me to be a reference for him. He got hired. Two months later, another, better opportunity came up. He asked me again to be a reference. I didn't hesitate to say "yes".

A reference is nothing more than asking someone to attest to whether or not somebody can do a job adequately. There is nothing unethical about someone wanting to move to a better position. Good opportunities don't grow on trees.