Welcome to the forum. Please add your location and your bike's model and model year to your profile so that you don't have to remember to tell us every time and we don't have to keep asking when you forget (see Forum Settings link in my signature).
And welcome to the world of antique vehicle ownership (they own us, not the other way around). Your bikes are about 4 decades old and may or may not have had all of the maintenance necessary to keep them safe & reliable so it is highly recommended to download the Factory Shop Manuals for your models (available through the CX Wiki - link in my signature) and go through all of the service procedures (at least on the parts you are going to use), regardless of whether the bike has reached the specified mileage.
I also recommend looking on all rubber parts with suspicion because rubber does not age gracefully. Before you think about using the tires that came with either bike check the date codes on them and if they are over 5 years old replace them no matter how good they look & feel (old rubber simply cannot flow around the irregularities in the asphalt well enough to grip, especially if it is cool or wet).
The same goes for the original rubber brake lines. They should have been replaced every 2 or 3 fluid changes (= 5 or 6 years) so I recommend shopping for modern stainless braided ones (they last practically forever and double the life of the fluid).
And don't forget things like the rad hoses and the boot between the engine and swingarm (they can crack on the bottom where you don't see it).
It may be too late but the best advice anyone can give you about customizing any vehicle is to get it safe & reliable in more or less original condition and use it for a while before you start making any changes so it can tell you what changes it needs to make it do what you want/need better. That approach almost always results in something you actually want to keep and use but making changes based on style or on what someone else (who may or may not really understand how the changes affect the way it works) has done often results in a piece of expensive yard art that you can't stand sitting on for more than a few minutes and might even be dangerous.
Personally, I think you would have been better off starting with a GL650 to end up with a 650 and a monoshock but I understand that you are trying to work with what you have.
People with more experience than me have described at great length why converting a CX500 swingarm that was designed to be supported by a pair of shocks to a single shock near the pivot point is not a good idea so I won't get into that (you can do your own research on the advisability of it).
But I will advise you that it is easier to make sure there is enough clearance between the tire and the frame now than it will be to change things after you hit a bump and find out the hard way. Before you go any farther set the shock at minimum preload and use a couple of ratchet straps between the frame and the swingarm to fully collapse the suspension and make sure that the tire won't hit the modified frame. Don't forget to leave room for a fender and to allow for a larger tire if you expect to use one (although fatter tires never handle as well as skinnier ones).