Tamsin with related to above query please find below suggestions.
1) I look at using DBsync to batch sync the email addresses for accounts across to QBOnline, so that we can send straight out of there? (If so, how? I have read the manual and can see that it is possible, but not HOW.)
On the Opportunity layout you have Primary Contact, if you enter the value in that than the respective contacts email ID will sync over to QBOE when new customers gets inserted, from there you can send invoices customers.If you want to update the customers information in quickbooks then it requires little mapping changing and also we need look into your DBSync account, for that contact support at support@mydbsync.com
2) Export my data from SF, mess around with it in a spreadsheet and then update QB from my spreadsheet?
You can update the email address information in QB through spreadsheet.Please note as long as your updating the Information to existing customers it will not be problem but if you create new records through spreadsheet the ids will be generated and hence it will mess the sync.
3) Build an invoice template in SF based on Receivable so I can create the invoice document in SF (using SDocs)
Yes you can create the doc using the information which is there in the receivables(You can refer to detail field which contains information of the respective invoice i,e customer name,address and the line items information in the xml format).Build the email template using that you can send invoices to clients.If you want this to be done by DBSync side then it comes under customization , to raise request contact support at support@mydbsync.com
As you want to handle the mail notification through Salesforce I would suggest third Option.