With several simple customizations, you can get this approach:

Define Users (logins) for each resource and configure their Home Company:

Create an Employee (linked to each User) and define the Timesheet Cost:

Create a Project, and remove the Company on the linked Analytic Account (to make it a global Analytic Account).

Create Tasks, where Employees can log their time ("resources from different subsidiaries collaborating on a Project"):

Periodically, review (and correct) the Analytic Items representing the Labor burden and generate an Accrued Payroll Entry  ("month end process and settlement for Time Sheets"):

Note: the first three lines you see here are Employee Expenses (already booked to a Financial Account). You would (if applicable) also see entries for each Vendor Bill line allocated to this project as well as any Customer Invoice lines for any project liabilities (deposits), earned (milestone payments) or accrued/deferred revenue.

For each Company, use the Generate Payroll Entry to record the Labor Burden:

Once you post the Journal Entries for both companies, you will see the financial account used in each Analytic Item, and a summary of the burden for labor (and in this case expenses) for each Company:

Balance Sheet for the United States Company ("how do charges feed into the Profit and Loss / Balance Sheet"):

Balance Sheet for the Canadian Company:

You would then Invoice your Customer, reclass the "in process" balance as needed, debit your payroll liability account when you create your Payroll Journal Entry, etc.

Customizations:

1. Minor modifications to screen design (hide/show fields, rename fields - done via Odoo Studio)

2. Automated Action triggered on the creation of each Analytic Line to ensure the Company recorded is the one from the Employee logging the time (to support multi-company time recording), and setting the Unit of Measure to hours (for readability).

3. Server Action "Generate Payroll Entry" that looks up the relevant CIP / PIP / WIP account, the relevant payroll accrual account and generates the weekly / monthly entry to burden the Analytic Account of the global project.