I don't really consider this to be a suitable answer, but I figured I would share this anyway in case someone ends up having the same problem. I was able to make two PowerShell commands that can be used to generate an SPSite.csv file manually that contains probably all of the relevant fields to make the app useful. Note: This workaround may be the victim of "over-engineering".
This first command needs to be run on a SharePoint server as a farm administrator user (access to the SP database):
Get-SPSite -Limit All | Export-CSV -NoTypeInformation SPSite-Export.csv
This second command can be run on that export to reformat it into one used by the SharePoint app. Note that a number of static values are being populated here, like the FarmId (which I blanked out in my example). You would need to update these fields to match your environment. Some of them I just had to guess on.
Import-CSV .\spsite-export.csv | Select @{Name="FarmId";Expression={'YOUR-UNIQUE-FARM-GUID'}},Id,_time,@{Name="Action";Expression={'Add'}},Url,AdministrationSiteType,AllowDesigner,AllowMasterPageEditing,AllowRevertFromTemplate,AllowRssFeeds,AllowUnsafeUpdates,AuditFlags,UseAuditFlagCache,EffectiveAuditMask,AuditLogTrimmingCallout,@{Name="AuditLogTrimmingRetention";Expression={'0'}},@{Name="AverageResourceUsage";Expression={'0'}},BrowserDocumentsEnabled,CatchAccessDeniedException,@{Name="CertificationDate";Expression={Get-Date -date $_.CertificationDate -Format u}},ContentDatabaseId,CurrentResourceUsage,DeadWebNotificationCount,HostHeaderIsSiteName,HostName,IISAllowsAnonymous,Impersonating,@{Name="LastContentModifiedDate";Expression={Get-Date -date $_.LastContentModifiedDate -Format u}},@{Name="LastSecurityModifiedDate";Expression={Get-Date -date $_.LastSecurityModifiedDate -Format u}},LockIssue,Port,PortalName,PortalUrl,Protocol,QuotaID,InvitedUserMaximumLevel,StorageMaximumLevel,StorageWarningLevel,@{Name="UserCodeMaximumLevel";Expression={'0'}},@{Name="UserCodeWarningLevel";Expression={'0'}},ReadLocked,ReadOnly,ResourceQuotaExceeded,ResourceQuotaExceededNotificationSent,ResourceQuotaWarningNotificationSent,RootWebId,ServerRelativeUrl,ShowURLStructure,SystemAccount,SyndicationEnabled,TrimAuditLog,UIVersionConfigurationEnabled,Bandwidth,DiscussionStorage,Hits,Storage,Visits,UserAccountDirectoryPath,UserCodeEnabled,UserDefinedWorkflowsEnabled,WebApplicationId,WriteLocked,Zone,Owner,SecondaryContact | Export-CSV -NoTypeInformation SPSite.csv
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