If all you want to do is provide a backup MX then you could use another Zimbra server and follow the instructions in any of these examples:
"backup mx" postfix - Yahoo! Search Results - don't forget that Zimbra uses Postfix as it's MTA.
I would not necessarily recommend you run a backup mx for your server it can be, as you've seen, problematic. Have you considered using an external provider to use as a backup site? There are companies that provide backup MX services (a google search should find them for you) or you could use an alternative approach.
I use a DNS hosting service for my domains (including the MX records) at easydns.com and as part of their package they provide a backup mail server. If your server goes down for any reason then the easydns mail server keeps your mail for up-to five days and when your server is back on-line it automatically forward the mail to your server - you don't have to worry about getting tons of spam, no additional server hosted elsewhere and it's in the cost of the DNS hosting package. There are plenty of companies that provide this type of service and again google is your friend. I have no connection with easydns other than as a satisfied customer of five+ years.