Ending Ceremony with telling guests to go home???

I agree with you. I would actually do both the before everything starts and in the program.
I would hate for my guests to think that they can hangout and mingle for awhile afterwards and then they get the moment of pure joy as we are announced husband and wife, the they get the "Oh BTW, kick rocks" announcement. I know it would be classier than that but I truly believe it would feel that way if you guys waited to say anything.

I honestly don't know how you'd tell them to leave without coming off rude.

If they know ahead of time, i would announce it again before ceremony starts, have it in the program, and have signs...then after the ceremony i would do your grand exit and let the officiant and tear down people start tearing down right away to give the guests a hint...if they start to chit chat, they can kick the guests out... you two are already gone, that way you are are not being rude... i feel like there is ALWAYS some people who don't get the social cues, lol

So I just attended a wedding ceremony and after the ceremony, the pastor announced that instead of doing a receiving line, they would release the pews one by one to have the guests take a picture with the couple. They had a cute wall set up in the back and a nice floral arrangement that separated us from the couple so we were socially distant but it wasn't awkward. Then we took our favor and left. I thought it was a cute idea and it helped move people along without them staying and mingling.

I think announcing at the beginning or end is fine, and I also agree that a zoom or other video streaming service ceremony might be better if you're that concerned about COVID.

"Our circle has a tendency to want to mingle." Of course they do! It's a wedding. If they are attending, that means they care about you and want to tell you congratulations, wish you well, etc. It would be the height of rudeness to tell them to leave without allowing for time to acknowledge their attendance, accept their good wishes, and thank them personally for coming. The pandemic doesn't excuse this rude plan at all.

So, no you are not overthinking this and it's definitely not appropriate. Make a plan for some safe, socially distant mingling and make sure to be very clear to guests what the plan is well in advance. Or change your plans and marry privately with a reception to follow when it is safe to party.

I agree with this

Even if you've already told your guests there will be no reception, I still think you need to be very clear that not only will there be no celebrating, but there will also be absolutely no socializing. Most people would not assume they won't be allowed to speak to you afterwards, and this plan seems very likely to cause many hurt feelings and be terribly awkward on the day.