Hi Matt,
Glad to hear the issue is resolved. I’d like to write a summary:
Problem
=================
You found there was 8 hours behind current local time when you created an Access Web App that contains a macro assigned to a button to Set Value of Property to =Now() of a Text Box (of field formatted as Date/Time) when clicked.
You have checked the timezone setting from regional setting of the SharePoint and local machine, both are set to London, and the timezone setting on your user profile is also set as "Always use regional settings defined by site administrators".
Troubleshooting
=================
1. We checked your local timezone and SharePoint regional setting and they all set as UTC timezone.
2. We recommended you save problem database as snapshot and create a new app to check if the incorrect timezone issue happened again. And then you feedback that there was no time difference on the new created app.
3. We tested locally and found the timezone of the access app should be consistent with regional setting of SharePoint site.
We suggested you upload the new app to SharePoint site.
4. As you failed to upload this problem app due to “a same version of this app has been existed” even you have deleted it from SharePoint site, we troubleshoot this issue from live meeting.
We resembled the troubleshooting steps as below:
#Issue 1
When we clicked “add app” and uploaded a local application package to SharePoint website, it indicated a same version application has been existed. While we have removed all access app from current site.
Troubleshooting
SharePoint site has two levels recycle bin, you may check it from “Site settings-->Recycle Bin-->End User Recycle Bin items|Deleted from end user Recycle Bin” or from link
https://support.office.com/en-us/article/View-restore-or-delete-items-in-the-Recycle-Bin-of-a-SharePoint-site-6DF466B6-55F2-4898-8D6E-C0DFF851A0BE
https://support.office.com/en-us/article/Restore-deleted-content-in-the-Recycle-Bin-of-a-SharePoint-site-5fa924ee-16d7-487b-9a0a-021b9062d14b
1. End-user delete the app from site content.
2. The app is moved to Recycle bin for the site where people can restore it or delete it.
3. If the app is deleted from the site Recycle Bin, it is sent to the Site Collection Recycle Bin, where an administrator can restore it or delete it permanently.

Solution
Remove deleted app from second stage recycle bin page and upload it again.
#Issue 2
After we uploaded the application to SharePoint site, we failed to open it due to permission issue.
Troubleshooting
We created new application and upload it to the same site, at this time, we could open the new application successfully, seems there is some permission issue regarding the data of this problem app.
1. We extracted the database from this app and found there are two tables inside and one of them is a linked table. There is records in non-linked table.
2. We opened the Access app in office access by selecting customize in Access from the settings gear icon in the app.
3. Created two new linked table to the same SharePoint list that was previous linked
4. When we’re prompted for authorization, click Trust it and click OK.
5. Delete the newly created linked table.
6. Save and publish, at this time, we could view the data from the non linked table, and we could not view the structure of another linked table from Office Access.
We confirmed with you got to know that one table is OK.
Solution
The authentication will be broke when we save the database as snapshot and upload to the website. We added two linked tables to authentication again from below link
https://support.microsoft.com/en-us/kb/3140416
#Issue 3
There was still 8 hours lag from local time after we opened the app.
Troubleshooting
We checked the timezone in regional setting and found it’s UTC -8, and the app time was consistent with this time zone.
And currently, the app was published in a sub site. We moved to the main site and checked the timezone in regional setting was UTC.
We did same things in issue 2 to publish this app and this time, there was no time different between app and local machine.
Solution
App timezone should be consistent with timezone in regional setting.
Root Cause
=================
Incorrect timezone in regional setting of SharePoint site.
Resolution
=================
Edited problem app and republished to SharePoint site. The timezone of new published app was consistent with current timezone of regional setting.
If you have any other questions, please feel free to post a new thread, and we will continue to assist you from there.
Regards,
James