Adjust time zone in Photos without adjusting time

So the problem is now in efficiency. Here's the situation: Let's say I have a bunch of photos from the east coast. The Date/Time stamp on all of them are correct but for some reason half have the EST time zone and half have the PST time zone.

What I want: to change all time zones to EST and keep date/time stamps the same.

I select all of the images and click to adjust date/time. Let's say the adjust date/time dialog shows the PST time zone (since the first images selected is PST), I then change the time zone to EST and change the date/time to stay as is (ignore the 3 hour time difference since I don't want timestamps to change).

Result: the system changes all timezones to EST (Good) and all timestamps to PST (Bad); so the result is that PST timestamps stay the same (correct) but the EST timestamps shift by 3 hours (incorrect)

To correctly do this, I have go through my images, one by one, to find the PST time zone images and adjust their time zones only. It's very tedious as there is no time zone filter. The only efficiency gain I get is if I find some PST images grouped together and I can do that subset all at once.

Thanks for the reply. I just tested and learned that I can select many photos and do as you suggested and though it shows a single date/time, the system will not adjust all photos to the displayed date/time but apply the offset to each photo keeping the original date/time. That works!