If we can't send the gateway info, is it possible to send something that identifies actual method, like Visa, Mastercard, etc?
No, as mentioned subscriptions are not tied to their baskets. So a subscription technically doesn't even have to have a payment. All emails and integrations trigger on subscription status not so much payment status.
You could use CB Auto Actions to send a custom email specifically when an offline payment is made though. The below should work, which is acting on a payment status change and not a subscription status change.
Global
Triggers: onCPayAfterPaymentStatusChange
Type: Email
User: Automatic
Access: Everybody
Conditions
Condition 1
Field: Custom > Value
Custom Value: [var2_gateway_account]
Operator: Equal To
Value: GATEWAY_ID_HERE
Condition 2
Field: Custom > Value
Custom Value: [var4]
Operator: Equal To
Value: Pending
Replace GATEWAY_ID_HERE with the ID of your offline payment gateway. This should send an email when it enters a pending status. You can specify whatever To address you like so it sends to your bookkeeper directly and a bonus is you can include whatever additional information you may need like username, user id, basket id, etc.. The variables for this trigger are as follows.
Code:
$_PLUGINS->trigger( 'onCPayAfterPaymentStatusChange', array( &$user, &$paymentBasket, &$subscriptions, $unifiedStatus, $previousUnifiedStatus, $occurrences, $autorecurring_type, $autorenew_type ) )
So with the above example var2 is $paymentBasket, which is their payment basket and var4 is $unifiedStatus which is the status of the basket.