How can I brighten an underexposed image in post without losing saturation from single-channel clipping?

You can't make pixels that are near clipping of any R, G or B any brighter than they currently are, so this limits brightening the brightest parts of the flower. You can brighten the less bright parts of the flower, though, trading contrast within the flower for actual (not just perceived) brightness.

If you need to brighten the parts that are close to clipping without losing saturation, you might want to use an extended color space if the hardware you want to present the image on supports it. In your specific case, changing from sRGB to Adobe RGB wouldn't help much, because going to Adobe RGB will mostly enable more saturated green, but the maximum saturation of red and blue keeps quite similar, so there is no brighter highly saturated red.

If you desaturate the highlights, you distribute some "red" brightness into "green" and "blue" brightness, which gives you headroom to increase the overall brightness. However, your goal is to not reduce the perceived saturation, so another way you could try is to not desaturate the highlights, but shifting the hue. RGB computer displays are way better at displaying a perceived saturated bright yellow than they are at displaying a perceived saturated bright red, mainly because the human eye is more sensitive to yellow than to red. So if you can tolerate a color change, making the orange more yellowish instead of reddish will also increase the headroom available for an overall brightness increase.

So, choose your poison:

• brighten only the less bright parts of the flower
• desaturate the red, at least in the brightest areas
• change the hue to be less faithfull to allow more brightness

Possibly, you achieve the best results by moderate application of all three strategies. In my experience, being moderate is the key point in making images look good without making them look artificial.