Sounds like textbook right upper mount broke. Common on many cars. Maybe struts are fine and it just needs a right upper mount. Mounts rattle subtly for a while when they wear and work loose, eventually turning into clunking like mad when they break, and at this point I agree unsafe to drive great distances. A full failure could even cause strut to pop into underside of your hood doing body damage on a good bump. But struts don’t usually clunk when they fail...they typically remain quiet and leak visibly, or seize up rigid, or fail the bounce test, all still mostly safe to drive with the possible exception of seizure. Mounts also don't need to be replaced in pairs, individual is fine. A broken mount also doesn’t mean there is a strut problem, nor does the strut need to be replaced if only the mount is bad. But strut needs to be removed from the car to access the mount anyway, it is an opportunity to replace...struts are indeed gradual wear items. And indeed struts themselves are recommended (not required) to be replaced in pairs due to this gradual wear characteristic...you want them to mostly match. Also agree any independent shop can handle this, if you’re gonna save $1200 over dealer prices for the pair and get the same parts, it highlights why I repeatedly put down dealer service departments on this site....
If your independent shop hasn’t personally diagnosed this car, and you have simply told them you need 2 new struts over phone, you may have done yourself a great disservice, especially if they have ordered the struts based exclusively on your word of a dealer diagnostic. My suggestion would be to have the independent shop diagnose and ask them specifically if they can just replace right front strut mount to stop the clunking and make car safe again. If they feel struts also need replacement, ask them to physically show you why. Again I’d want to see oil leaking, or seizure, or a failure of a bounce test. Absent one of these 3, the struts are still working fine and neither needs replacement.
Unfortunately if shop has already ordered struts from Honda we might be in a restocking parts fee situation If it doesn’t actually need them. Might lose 15% of parts cost if you and independent shop decide they can be returned to Honda and not installed. That’s money out the window but it’s an 85% parts savings for possibly unnecessary expensive parts. Drink the 15% poison if necessary.
Mount alone maybe $60 plus 2 hours labor? $250 to $300 bottom line repair at most shops. No alignment necessary either, the mount sets in fixed holes and there is no upper adjustment. Alignment might be acceptable anyway on a high mileage car, but consider it an optional extra cost if you want to save another $99 or so add on.
Hard for me to diagnose over internet, but I have a lot of questions here based on what you have said...I see high likelihood of unnecessary pair of struts being installed here and am 75% confident a single strut mount replacement would get your car solidly back on the road again for about 10% of what the dealer quoted you.