Redirect customer to specific order checkout later
Sounds to me like the sandbox isn't using pricing rules to set the "new offer."

Here's what I would do (without knowing what the sandbox is doing):


I would create a custom line item type using commerce_custom_product
I would then add a price field called "price_override"
I would then create a pricing rule that overrides the original price of the line item with the "overridden price" if it exists.
I would then make sure that the sandbox or a custom module sets that line item field when a new offer is made


The above approach has the benefit that the price is actually using pricing rules, but the "custom price" is per-line-item instead of per-order. Now it might be possible, depending on how the sandbox is functioning, to access the "custom pricing" and use it in a pricing rule. But the same approach would still be taken above. 

// Edit

You can always just send users to "/checkout" ... but likely they would need to be logged in first to be connected to their order (this would be based on default permissions). So I would use the Drupal system to your advantage, this little link will present anonymous users with a login form, then redirect to checkout (and will simply redirect to checkout if logged in):

/user/login?destination=checkout