Yes you can get them mounted at a car place. That is what I did. Pulled the wheels and took them to have the tires installed.
Looked for BBB A+ rating and good reviews. Talked to them about how particular I was but even at that there were still some gouges in the rims. Not huge but there were several and very noticeable to me at least. I was not happy! Spoke to the owner who said they have a disclaimer about damage to 'custom wheels' but I pointed out that the counterman said they could mount with no damage. After consultation they agreed to send the wheels to a local wheel repair place called 'Wheel Tech.' This was on a Friday afternoon. Over the weekend I investigated Wheel Tech and saw some of the high end cars with damaged and broken wheels they had repaired so I felt a bit better. No idea how they did it - did not dismount the tires - but when I got them back Tuesday morning they looked great. Better than new even.
So what to conclude? I have no idea and no idea how I'll proceed when I have to replace these. Might see if the Harley dealer would do it. But since this is my first rodeo with rear trike tires I have no idea what would have happened if I'd had the Harley dealer do it.
Added: I'm not all that knowledgeable about mounting tires but I asked the owner why they could not remove and install from the back side of the rim. He took me to the machine (like all the others I've seen over the years) and explained why that was not possible. Can't recall the reasoning but it seemed to make sense to me at the time. And the gouges on the outside edge of the rim was of course from the tools that break the bead and run around the rim to remove and mount the tire.