Image in Lightroom Develop Module looks dramatically different than image in Library module or exported image. How do I fix this?

Forgive me, I know this has been discussed at length, but (partly due to my ineptitude) I'm unable to figure it out.

My issue is:

I work on an image in the develop module and when I become satisfied with it, I export it. The exported image loses clarity and becomes lighter. I am exporting the image as a Jpeg (I've tried other formats too) at 100% and have tried every color space variation but have gotten the same disappointing results. The exported image is identical to how the photo looks in the library module, not the develop module. This is very frustrating, because I want it to appear identical to the image on the develop module (since that's what I have control of). It seems pointless to put all this effort into editing the image to have the export look so different and then need to over edit your photo in hopes of making the library/export image look how you want it. It doesn't make sense.

I've read various, confusing things about how to remedy this.

The first photo is a screenshot of the Develop Module (How I want the export to look), the second one is the library (How the export actually looks). As you can see, the top one is darker and sharper.

Some stuff I've read:

1. The library module uses a different color spacing than the develop module and for them to look the same, I need to properly calibrate my screen. I don't have Spyder or any external products to calibrate the screen but I did attempt to do it through my MacBook Pro's settings. I've tried many different variations of this but have never been able to have the develop image look the same as the library/export. Beyond that, it doesn't seem to make sense that calibrating the screen would fix this since I'm looking at these images on the same screen, no? Even if the screen is improperly calibrated, both images would be viewed on the same screen, so how would that cause a disparity in how they look?

Also, is there a way to adequately calibrate my screen without having to buy a pricey product like Spyder?

2. The library module and export will apply noise reduction which changes the appearance of the image. This seems to be true and I tried reducing the noise reduction in the develop module, in hopes of making the library/export image look the same, but I didn't achieve the results I was looking for.

3. People have pointed out that the Library and Develop module do look identical when both are viewed at 1:1 ratio. This is true, but it seems to be a moot point. They may be identical at a a 1:1 ratio, but the export isn't meant to be viewed that way. I'm putting these images on the web, so yes, theoretically the export will look identical to the develop module's image when magnified to 1:1, but nobody will be viewing it at that level of magnification.

Basically, I just want my exported photo to look like what I've worked for in the develop module. Is this possible? How? I'm at a loss here.