Do you have any local camera shops that print? Mine has a wide format printer with several paper options. It might cost a few more bucks compared to a large online service, but the hands on in-person attention they can give might be totally worth it for you.
Have you tried cropping your photo to the aspect ratio of a 16x20in print? You will lose the nice symmetrical reflection. I'd stick with a 3:2 aspect ratio to preserve the composition- 12x18in, or 13.5x20in (not a standard paper option, but you can cut down a 16x20) or 16x24in.
Regarding the resolution, I recently saw a show of 11x14in prints made with a relatively ancient digital camera, a 3mp model from 2001. At 1ft away, the pixelation was noticeable. At about 3ft away, it stopped mattering and content overruled any little technical flaws. Resolution will not be a problem for printing your egret at the sizes you're talking about.
Good luck with your printing adventure
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